Preheat oven to 325ºF. Line two 8-inch square baking pans with foil, leaving a 2-inch overhang on 2 sides. Mist both pans with cooking spray.
In a large heatproof bowl set over a saucepan of simmering water, melt butter and chocolate together, stirring often. In a small cup, stir together vanilla and espresso powder until dissolved. Remove bowl from saucepan and whisk in sugar, brown sugar and espresso mixture. Whisk in eggs until batter becomes smooth and glossy. Stir in flour and salt, mixing batter just until combined.
Divide batter between baking pans, spreading with a small spatula. Batter will be shallow in pans. Bake until just done, about 15 minutes, rotating pans halfway through. Do not overbake. Place pans on a wire rack to cool.
Soften ice cream in fridge for 15 minutes. Spoon ice cream over 1 pan of brownies, spreading evenly with a small spatula. Unmold second pan and peel off foil. Press brownies, bottom side down, over ice cream. Cover with foil and freeze until firm, about 5 hours.
Remove pan from freezer. Use foil overhang to pull out brownies. Place on a cutting board, flip over and peel off foil. Trim edges, cut in half, then cut each half into quarters. Serve immediately.