Bake the brownies for 17 to 20 minutes until the batter is set but still soft. Transfer the sheet pan to a cooling rack and let it cool for 5 minutes. Cut the brownie in half crosswise and let it cool completely in the pan and then transfer the two large pieces of brownie to a large piece of parchment paper.
Let the ice cream sit on the counter for about 20 minutes so it softens slightly, but does not start to melt.
Spread the softened ice cream evenly over one half of the brownie. Top with the other half of the brownie and push down firmly. Wrap in plastic and freeze for 2 hours.