Step 1

Whisk cocoa powder, salt, baking powder, and 2½ cups flour in a medium bowl. Using an electric mixer on medium-high speed, beat butter, brown sugar, and granulated sugar in a large bowl until light and fluffy, about 4 minutes. Reduce mixer speed to medium and add eggs and vanilla; beat until very fluffy, about 30 seconds. Reduce speed to low and gradually add dry ingredients, beating just until combined (use a large spatula to incorporate any dry ingredients at the bottom of the bowl). Divide dough in half and wrap each in plastic, pressing down to form into ½”-thick disks. Chill until firm, at least 2 hours.

Step 2

Preheat oven to 350°. Let 1 disk of dough sit at room temperature until softened slightly, about 5 minutes. Roll out on a lightly floured piece of parchment paper into a large ⅛"-thick rectangle (about 16x12"), dusting with more flour as needed. Use a knife and a ruler (precision is key) to cut into 4x1½" rectangles, then use a thin metal spatula to transfer rectangles to a parchment-lined baking sheet, spacing 1" apart. (If at any point the dough becomes too soft and sticky, slide dough with parchment onto a baking sheet and chill until firm.)

Step 3

Chill dough on baking sheet while you repeat the process with the second disk of dough. You should end up with 30 cookies total. Save scraps for another use or discard. Prick cookies in several places with a fork. Bake, rotating baking sheets front to back and top to bottom halfway through, until edges are firm, 12–15 minutes. Let cool on baking sheets. Turn half of cookies over.

Step 4

Line a 13x9” baking pan, preferably straight sided, with 2 layers of plastic wrap, leaving several inches of overhang on all sides; place in freezer. Remove both pints of first ice cream flavor from containers (just peel away container if it’s paper, or use a rubber spatula to help slide ice cream out intact if container is plastic). Cut ice cream into 2” pieces and place in a large bowl. Let sit until slightly softened, about 5 minutes, then stir with a wooden spoon or a large rubber spatula until the consistency of thick cake batter. Scrape ice cream into chilled pan and smooth into an even layer with a small off-set spatula. Freeze uncovered until firm, 15–20 minutes.

Step 5

Repeat softening process with both pints of second flavor.

Step 6

Scrape second flavor over first layer and smooth out, spreading ice cream all the way to the edges and making top as level as possible. Cover with plastic wrap and freeze until ice cream is hard, at least 8 hours.

Step 7

Remove ice cream from freezer, unwrap, and invert onto a cutting board; remove pan and peel off plastic. Trim sides of ice cream block to make a neat, straight-edged rectangle measuring 12x7½” (yep, there’s that ruler again). Working quickly so ice cream doesn’t melt, cut block lengthwise into 5 equal rows and then crosswise into thirds so you have 15 pieces measuring about 4x1½” Working with 1 brick of ice cream at a time, use a thin metal spatula to place on a flat-side-up cookie and top with a right-side up cookie. Transfer sandwiches to a rimmed baking sheet set in the freezer as you work. Freeze sandwiches until ice cream is hard, about 2 hours. Cover tray with plastic wrap and freeze at least another 8 hours to let cookies soften.

Step 8

Do Ahead: Dough can be made 2 days ahead; keep chilled. Cookies can be baked 1 week ahead; transfer to a resealable plastic bag and freeze. Layered ice cream can be made 1 week ahead; keep frozen in pan. Sandwiches can be assembled 5 days ahead; keep frozen.