1. Remove paper carton from ice cream block. Place block on a long side on cutting board. Using sharp knife, slice off lengthwise six 1/2-inch-thick rectangles; return remaining ice cream to freezer. Lay slices flat on waxed- paper-lined baking sheet. Freeze 45 minutes, until firm.
2. Meanwhile, heat oven to 350 degrees F. Stir cake mix, eggs, oil, cherries and extract in bowl until dough comes together. Divide into 24 pieces, about 1-1/2 tablespoons each. Roll into balls. Place 3 inches apart on ungreased baking sheets, about 8 balls per sheet. Flatten each into a 3-inch circle; if sticky, grease bottom of glass.
3. Bake in 350 degrees F oven 10 minutes, until firm. Cool on sheet 2 minutes. Transfer cookies to rack to cool.
4. Remove ice cream slices from freezer. Using 3-inch round or scalloped cookie cutter, quickly press 2 rounds out of each ice cream slice, for total of 12 rounds. Save ice cream scraps for snacking. Using spatula, transfer 1 ice cream round onto 1 cookie; top with another cookie. Wrap in plastic wrap. Repeat, using all rounds and cookies. (If ice cream begins to melt, freeze.) Freeze.