Pre-heat your oven to 350 degrees. Line two square 9x9 inch baking pans with parchment. (I like to overlap the parchment, so there’s ZERO chance of sticking.) If you only have 1 pan, don’t panic, you can cook your layers one at a time.
Starting with the brownie layer! Melt the butter in a medium saucepan over medium-high heat. Once melted, remove from the heat and whisk in the white sugar and cocoa powder until dissolved. Add the salt, vanilla extract, and eggs, whisking continually until the eggs are well combined. Add the flour and mix until incorporated.
Pour the brownie batter into one of the prepared pans and use a spatula to make sure that fills the pan in an even layer. Set aside while you prepare the cookie layer.
Now it’s time to make that cookie dough. Place the butter, brown sugar and granulated sugar in a mixing bowl. Use a handmixer to cream the butter and sugars together until light and fluffy, about 3 minutes. (You can also use an electric mixer fitted with the paddle attachment, but for such a small quantity of dough, it may not be worth breaking out that bad boy.) Add the vanilla and the egg and mix well, scraping down the bowl regularly. In a small bowl, sift together the flour, baking soda, and salt. With the mixer on low, slowly add the flour mixture to the butter mixture. Fold in the chocolate chips with a rubber spatula.
Place the cookie dough into the other prepared baking pan, and use a spatula to spread it into an even layer.
Transfer both the brownie and cookie layers to the oven. Remove the cookie layer after 13 minutes. Continue baking the brownie layer for another 10 minutes (23 minutes total).
Let both the brownie and cookie layers cool COMPLETELY. Pop them in the freezer to speed up the process if you like.
Now it's time to assemble the ice cream sandwiches. Remove the brownie layer from the parchment, flip it over, and return it to the parchment lined pan. (This is so the nice crackly side of the brownies will face outward.) Use a spatula to spread the softened ice cream in an even layer over the brownies.Carefully remove the cookie layer from its pan and place it on top of the ice cream. Cover with plastic wrap or tin foil and freeze for at least 4 hours.
When ready to serve, run a clean, sharp knife under hot water and slice the "cake" into 9 3x3 inch sandwiches.