Ray (WOODY ALLEN) and Francis "Frenchy" Winkler (TRACEY ULLMAN) have been married for twenty-five years, but Ray's not satisfied with his life. An ex-con and current dishwasher, he and his two buddies, Denny (MICHAEL RAPAPORT) and Tommy (TONY DARROW), have hatched a plan to better their lives. Needing to contribute six thousand dollars apiece, they plan to lease an empty pizza store and then dig a tunnel from it, underneath the adjoining store, and then up into the vault of the neighboring bank.
Frenchy, a manicurist by trade, isn't crazy about the plan. That's not only because that's a big chunk of their savings, but also because she knows that neither Ray nor his buddies are the brightest bulbs on the planet. When the trio learns that someone else has already leased the space, however, they hope they can sweet talk their way into getting the space. Unbeknownst to them, a fellow ex-con and habitual arsonist, Benny (JON LOVITZ), has already nabbed the spot.
Not surprisingly, after hearing their plan, Benny immediately wants in on the action. To cover for the noise they'll be making in the basement, they decide to have Frenchy sell cookies upstairs as a front. As they bungle their way through their efforts of tunneling to the bank, Frenchy's cookie business suddenly becomes the hot spot in town, eventually becoming so busy that they hire Frenchy's dimwitted cousin, May (ELAINE MAY), to help out.
A year later, the men have dropped all plans of crime as Frenchy's cookies have become so popular, she and Ray have gone corporate and become extremely wealthy executives. Although Ray is uncomfortable with their new trappings and lifestyle and wants to return to the way they were, Frenchy couldn't be happier, although she realizes she's not refined enough to fit in with the upper crust.
Thus, she hires David (HUGH GRANT), a suave/debonair art dealer who agrees to teach her about all of the better and more refined things in life. As such, and with the couple growing apart, it's only a matter of time before Ray's criminal longings have him plotting another heist.