Special equipment: a 3 1/2- to 4-inch fluted round cookie cutter
Directions
Beat together butter and sugars in a large bowl with an electric mixer until pale and fluffy. Beat in egg, vanilla, baking powder, salt, cinnamon, and cardamom. Add flour and cornmeal and stir with a wooden spoon until just blended.
Halve dough and pat into 2 disks (dough will be very soft). Chill, wrapped in plastic wrap, at least 4 hours.
Preheat oven to 350°F.
Roll out 1 piece of dough between 2 sheets of wax paper to 1/4 inch thick. Remove top sheet of wax paper and cut 3 cookies with fluted cutter, leaving cutouts in place. Replace wax paper. Roll out remaining piece of dough and cut 3 more cookies in same manner. Chill both pieces of dough until firm, about 15 minutes.
Carefully transfer cookies to an ungreased large baking sheet and keep chilled. Reroll scraps between 2 sheets wax paper and cut out 2 more cookies (for a total of 8; you'll have 2 extra in case of breakage). Transfer to baking sheet with other cookies.
Bake cookies in upper third of oven until edges are golden brown, about 20 minutes. Transfer to a rack and dust with confectioners sugar.
Melt butter in a large nonstick skillet over moderately high heat, then add brown sugar and lemon juice and cook, stirring, until smooth, about 1 minute. Add fruit and bourbon (if using) and sauté, stirring occasionally, until fruit is tender, about 5 minutes (sauce will be red). Remove from heat.
Place 1 cookie on each of 6 dessert plates and dust again with confectioners sugar. Spoon some warm fruit topping over each cookie, then top with a scoop of ice cream.
