In the United Kingdom, Daisy May Cooper is a certified television star, a familiar enough presence as both an actress and series creator that she appeared on the British version of The Masked Singer earlier this spring. She was the Otter.

Had Cooper been revealed on the American Masked Singer in February, Jenny McCarthy probably would have been totally flummoxed. Cooper might have been familiar from a pair of Armando Iannucci projects — The Personal History of David Copperfield and Avenue 5 — but instead of This Country, an award-winning comedy she starred in and created with brother Charlie, we got U.S. remake Welcome to Flatch; and instead of the British smash hit Taskmaster, on which Cooper contributed to the 10th season, we got the American version of Taskmaster, which bombed in its lone Comedy Central season.

That’s changing, of course. American audiences are getting a crash course in Daisy May Cooper this spring, letting us catch up on this incredibly talented multi-hyphenate.

It’s probably for the best that Cooper’s first big domestic showcase was Cash Carraway’s HBO dramedy Rain Dogs, a scathing and effectively miserable exploration of economic desperation and found families in contemporary London. It’s a tonally challenging show held together by Cooper’s broad-but-grounded central performance.

Cooper’s second star vehicle of the spring is Hulu and BBC One’s Am I Being Unreasonable? which may be even more totally challenging. Created with co-star Selin Hizli, Am I Being Unreasonable? is a comic thriller or a silly mystery. It’s a showcase for many of the same performance traits that make Cooper so watchable in Rain Dogs and it’s a fully engaging show to follow and attempt to figure out. At the same time, it’s a show that, in its attempts to be structurally ambitious, undermines its emotional core. It’s a story of two friends bound by complementary trauma that’s too often turned into a guessing game.

Am I Being Unreasonable? features Cooper as Nic, a suburban mother stuck in a psychological rut. She loves her precocious son (Lenny Rush’s Ollie), but her marriage to Dan (Dustin Demri-Burns) is in what seems to be a permanent rut and she’s viscerally haunted by the shocking loss of her true love, Alex (David Fynn), a grief she can’t share with anybody. Certainly she can’t share her feelings with Dan or with her ultra-annoying neighbor (the hilariously scene-stealing Karla Crome).

Then Jen (Hizli) shows up in town. She’s a put-upon mother as well. She hates the same fussy mums as Nic does. Soon, with a healthy alcoholic assist, Nic is telling Jen things she probably shouldn’t be telling Jen, because Jen has secrets of her own and it’s more than possible that there might be downsides to their seemingly therapeutic friendship.

The first thing to know about Nic, as a character, is that she’s very funny and she’s very damaged, and if that seems like two things to know about Nic, they go hand-in-hand. Nic is experiencing flashbacks and hallucinations and bouts of rage that, while completely justifiable, aren’t helping her make friends and influence people. Like Costello, Cooper’s character in Rain Dogs, Nic is a dedicated mother, but her monomaniacal concern that she’s raising a child likely to emulate her greatest flaws isn’t exactly wrong. Cooper has very quickly proven herself to be an exceptional performer opposite child actors and she and Rush have scenes together that are very silly and very sweet in equal measure, and then a bit disturbing when you take a step back and reflect.

Hizli may have the more difficult role because for a long time it isn’t clear what Jen really is. Is she just a lonely new woman in town? Is she looking for a friend or is she out for revenge or something else? Hizli blends a sweet sadness with manic glints that open the door for various interpretations, and if the character remains sympathetic while keeping you guessing as to her every motivation, that’s to Hizli’s credit.

The guessing game aspect of Am I Being Unreasonable? is what keeps the show going and what I ultimately found frustrating. The entire series is driven by the withholding of information.

Sometimes it’s organic. Nic is in denial about many things and she knows things that, for increasingly obvious reasons, she can’t tell anybody. Jen is possibly in denial and possibly self-deluded, but it’s equally obvious why she can’t just come out and announce her backstory.

Still, the series becomes more invested in inserting narrative gaps that exist only to have that information filled in later in the series. If all I’m thinking is, “Oh, that’s why that plot hole wasn’t a plot hole!” or “Oh, that wasn’t a character inconsistency at all!” then I’m approaching the series as a puzzle, which it absolutely is, and not as a character study, which it probably should be.

The show has abrupt mini-shifts in genre — that Ollie is an aspiring filmmaker with an amusing horror fixation helps justify some things — and these jarring, nightmarish detours would probably be enough differentiation without treating the narrative and its exclusions as something to be solved. Instead, there are bigger issues and character dimensions getting lost thus far.

Am I Being Unreasonable? has already been renewed for a second season. I’ll be interested to see if these first six episodes — a wonderfully brisk season at 30 minutes per episode — are just a whiplash-y introduction to make it clear that anything could happen with these characters, but not a template for the structure going forward. Spending more time with these two main characters as people and not pieces in a shifting sleight-of-hand exercise might give the strong performances a chance to assert themselves more. Then again, the show might not have much of an engine without its trickery. Reservations here aside, I’m enjoying the American Spring of Daisy May Cooper. And be sure to check out Rain Dogs.