Eight 1-1/2-inch squares chewy brownies (about 1/2-inch thick)
1 cup coffee ice cream
3 large egg whites
Pinch of table salt
1/2 cup sugar
1/4 teaspoon vanilla
Press down gently on the brownie squares until they are about 1/3-inch thick. Working very quickly, place 1/8 cup ice cream on top of each of four of the squares, spreading it to cover the brownie and top the ice cream with a second brownie, pressing down gently. Wrap the ice cream sandwiches tightly with plastic wrap and freeze them for 2 hours.
About 30 minutes before serving, place the egg whites in a medium metal bowl set in a larger bowl of hot water to bring them to room temperature quickly. Preheat the oven to 450 degrees. Remove the bowl of egg whites from the larger bowl and, using electric beaters, beat the egg whites on low until frothy, add the salt and continue beating on medium just until they form soft peaks. Add the sugar gradually in a steady stream, beating until the mixture forms soft glossy peaks. Beat in the vanilla. (These egg whites will not be cooked to 160 degrees, which is the safety zone for killing salmonella, so substitute pasteurized egg whites if you are concerned.)
Place the ice cream sandwiches on a parchment-lined rimmed sheet pan and, working quickly, coat the sides and top of each one thoroughly with the meringue so that there are no gaps. The meringue will insulate the ice cream and keep it from melting so quickly in the oven. Either smooth the meringue or make peaks, depending on the finished look you want. (Note: You will have slightly more meringue than you need.)
Bake the frosted cakes on the middle shelf of the oven for 4 to 5 minutes or until golden. Transfer to four plates and serve right away.