Preheat and Prep: Preheat your oven to 350°F (177°C). Line one 9-inch square baking pan with parchment paper, leaving enough overhang on the sides to lift the warm brownies out later. Set it aside.
Melt and mix: In a microwave-safe bowl or a small saucepan on the stove, melt the butter. Whisk in the sugar until it's completely combined, then whisk in the eggs and vanilla. The batter will look a little dull and that's perfectly normal.
Fold the dry ingredients: Add the cocoa powder, flour, salt, and baking powder. Fold everything together with a rubber spatula or wooden spoon. It will come together, I promise. The batter will be very thick — you should have about 4 cups total.
Spread and press: Spoon and spread half of the batter (about 2 cups) into the prepared pan. The batter is thick and heavy, so do your best to spread it evenly. I find the back of a spoon works best. Place a small sheet of parchment paper directly on top of the batter, smoothing it down gently.
Bake: Bake for 15-16 minutes. I find any longer over-cooks the brownies, making the sandwiches difficult to cut and eat. Remove from the oven and cool for 5 minutes in the pan. Carefully, using the parchment overhang, lift the warm and soft square sheet of brownies out of the pan as a whole. Set it aside.
Repeat: Line the warm pan with another sheet of parchment paper, leaving overhang. Give the remaining batter a stir — it will be very thick. Add a teaspoon of water if necessary to thin it out, but no more. Spoon and spread it in the pan, place parchment on top, and bake for another 15-16 minutes. This time, let the brownies cool for 15 minutes in the pan. During this cooling time, take the ice cream out of the freezer so it has a chance to soften.
Assemble: Scoop the softened ice cream onto the warm brownie layer in the pan. You'll use almost all of the half-gallon. Using the back of a spoon or your ice cream scoop, gently spread it into an even, thick layer.
Top and freeze: Carefully pick up the first square sheet of brownies and place it on top of the ice cream layer. Gently press it down into the ice cream to help it stick. Cover the entire pan with aluminum foil or plastic wrap and freeze for at least 12 hours and up to 1 week. I find 12-18 hours is the perfect amount of time.
Slice and serve: Remove the pan from the freezer. Lift the whole block out using the parchment overhang. Using a very sharp knife and some arm muscle, cut into 12 squares. Enjoy immediately.