Preheat the oven to 350°. Line both 9 inch square baking pan with parchment paper, leaving enough overhang on the sides to lift the warm brownies out. Set aside.
In a large sauce pan on the stove, melt the butter. After melting, whisk in the sugar until completely combined. Then, whisk in the eggs and vanilla. The batter will look a little dull and murky.
Remove from heat and add in the cocoa powder, flour, salt and baking powder. Fold it all together with a siicon spatula. Batter will be thick and makes about 4 cups.
Spoon and spread half of the batter about 2 cups into each prepared pan. Using the back of your spoon or spatula, spread the batter evenly into each pan. Place a small piece of parchment paper directly on the top of the brownie batter, smoothing it down. The top parchment paper helps the brownies stay flat while baking and not rising as much.
Bake each pan separately for 15 minutes. Any longer will make the ice cream sandwiches difficult to cut. Let cool for 15 minutes and remove one pan of brownies out of the baking pan (this one will go on top of ice cream).
Scoop the softened ice cream on top of the one layer of brownies. Spread evenly with back of spoon. You will use almost all of the ice cream.
Carefully pick up the first brownie square sheet of brownies and place on top of the ice cream layer. Gently press it down into the ice cream to help it stick. Cover with plastic wrap and freeze for at least 12-18 hours. Any less and the ice cream will be to soft. Longer than 18 hours the sandwiches are hard to cut.
Remove the pan of ice cream brownies from the freezer. Carefully lift them out as a whole using the parchment paper overhang on the sides. Using a very sharp knife, cut into sqaures or rectangles. Serve and enjoy immediately!