Adjust the oven rack in the center of the oven and preheat to 350 degrees F. Sift the flour, baking powder, baking soda, and salt into a medium mixing bowl. Set aside. Place the butter, granulated sugar, and light brown sugar in the bowl of an electric mixer and cream the ingredients on high speed. Add the vanilla and egg to the mixer and mix on medium speed. Stop the mixer and scrape down the sides of the bowl with a rubber spatula. Add the flour mixture and combine on low speed.
With a tablespoon, form the dough into balls, using about 2 spoonfuls for each. Divide the balls of dough among 3 large baking sheets and press to slightly flatten. (The cookies should be about 2 inches apart or 8 cookies per baking sheet.) Press 5 or 6 chocolate candies into the top of each cookie, if desired. Bake in batches in the oven until golden around the edges, about 13 minutes. Remove the cookies from the oven and allow them to cool for 2 minutes on the baking sheets. Transfer cookies to wire racks and cool completely. You will need 12 cookies for the ice cream sandwiches. Extra cookies can be stored in an air-tight container or enjoyed immediately.
To build the ice cream sandwiches, soften ice cream at room temperature for 15 minutes and line a baking sheet with parchment or waxed paper and set aside.
Using a small, tablespoon-sized ice cream scoop, place 3 to 4 scoops of ice cream on the bottom side of one cookie. Working quickly, top with a second cookie and press lightly to push the ice cream to the edges of the cookie. Use a small spatula to smooth the ice cream around the edges of the sandwich. If using sprinkles, place sprinkles in a shallow container and roll the edges of the ice cream in the sprinkles, pressing lightly to coat.
Place ice cream sandwiches on the prepared tray and freeze immediately, until firm, about 2 hours.
Yield: 6 large ice cream cookie sandwiches