Remove the ice cream from the freezer and allow it to soften slightly, about 5 minutes. Place it in a large bowl and stir it until it's the consistency of thick buttercream frosting.
Line a 9 by 13-inch* cake pan with plastic wrap, letting it overhang. Scrape the ice cream into the pan and smooth it out with an offset spatula. Cover with another piece of plastic wrap directly on the ice cream and place the pan in the freezer to freeze for several hours, at least 4, or overnight. *You can also use two 8 by 8 or 9 by 9-inch square cake pans and put different flavors of ice cream in each.
MAKE THE COOKIE DOUGH
Whisk the gluten free flour blend, unsweetened cocoa powder, salt, and baking powder in a medium bowl until well combined. Set aside.
Cream butter with sugars until light and fluffy, about 4 minutes. Add eggs and vanilla and continue to beat until fluffy, about 2 minutes. Slowly add the flour mixture on low speed and pulse just until combined. Use a spatula to incorporate any dry ingredients left in the bottom of the bowl.
Divide dough in half and wrap each in plastic wrap. Refrigerate for 2 hours.
BAKE THE COOKIES
Preheat the oven to 350° F. Remove the dough from the refrigerator and allow it to sit for about 5 minutes to soften slightly. Roll out on a lightly floured piece of parchment paper (or between two sheets if it's extra warm in your house) to about ⅛-inch thickness and cut into rectangles (or use cookie cutters to cut out desired shapes). You may need to refrigerate after rolling out (before cutting) if it's warm in your house. This is a slightly sticky dough.
Transfer cutout cookies to a parchment-lined baking sheet and place in the refrigerator to chill while rolling out the other disk of dough.
Bake the chilled cookies until the edges are firm, about 12 minutes. Let cool completely on baking sheets. Flip half the cookies over.
ASSEMBLE
Remove the ice cream from the freezer and cut into equal-sized rectangles (or use the same cookie cutter as you used for the cookies) and place ice cream on the overturned cookies. Top with another cookie and press lightly to adhere.
Wrap sandwiches and freeze overnight, until ice cream is hard and the cookies are slightly softened. The longer the cookies sit in the freezer, the more the cookies will soften so they're perfect for make ahead.
Notes
Ice cream sandwiches will keep in the freezer, well wrapped, for up to three months.