1. Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper.
2. In a small bowl, whisk together the flour, cocoa powder, salt, and baking powder. In another bowl, beat the butter, shortening, and sugar together with an electric mixer until fluffy. Beat in the eggs and vanilla, beating until smooth. With a spoon, stir in the flour mixture, stirring just until you have a smooth dough.
3. Using a 2 tablespoon cookie dough scoop, drop 6 mounds of dough on each baking sheet, leaving a couple inches between each cookie. Bake until the cookies are firm around the edges and soft in the middle, about 15 minutes. (For even baking, rotate the pans from top to bottom and back to front halfway through baking.) Using a spatula, transfer the cookies to a wire rack and cool completely.
4. Meanwhile, turn the ice cream pints on their sides and use a serrated knife to slice through the containers, cutting each into 3 even rounds. Place the ice cream disks on a baking sheet and freeze until ready to assemble the sandwiches.
5. To assemble, peel the cardboard from the ice cream disks and sandwich each disk between 2 cookies. Serve the sandwiches immediately, or wrap individually in plastic wrap and freeze up to 1 week.
The bottoms of some ice cream containers have a little lip to them, so take that into consideration when you are cutting the ice cream to make sure you get disks of even size.
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