Preheat oven to 350 degrees. Butter a 10-by-15-inch jelly-roll pan. Line with parchment, leaving a 2-inch overhang on short sides, then butter paper.
In a medium bowl, whisk together butter and sugar, then whisk in eggs and salt. Add flour and cocoa and mix until just smooth. Spread in pan. Bake until brownie is dry to the touch and edges have begun to pull away from pan, 10 to 12 minutes. Let cool 5 minutes. Using paper overhang, transfer to a wire rack and let cool completely.
Transfer brownie to a work surface and cut in half crosswise. Cover pan with a large sheet of plastic wrap and place one cake half on it. Spread with ice cream, invert remaining brownie half on top, and wrap tightly in plastic. Freeze until firm, about 2 hours.
Unwrap, cut into 12 pieces, and serve.
Want More Chocolate?
Dip half of each sandwich in melted chocolate, freeze to set, and enjoy. We love the combo of the chocolate brownie and mint-chip ice cream, but you can use any flavor in your sandwiches.