With its crisp chocolate shell and chewy brownie base, this ice-cream bar is a treat to bite into.
Heat oven to 350 degrees. Line a 10-by-13-inch pan with parchment paper. Bring a small saucepan of water to a boil; turn off. Combine 1 1/2 sticks of butter and 6 ounces of chocolate in a small heat-proof bowl; set over saucepan. Let stand, stirring occasionally until chocolate is melted and smooth.
Whisk the eggs together in a large bowl; add salt, sugars, and vanilla, and stir to combine. Stir in the butter-and-chocolate mixture, then fold in flour. Pour the batter into prepared pan, spread evenly, and place in oven to bake until top is shiny, about 20 minutes. Do not overbake; a cake tester should not come out clean.
Set the brownie aside; let it cool completely. Store in an airtight container overnight. The next day, loosen corners of brownie. Lift it from pan, keeping brownie intact. Invert onto a cutting board, and peel off parchment. Trim about 1/4 inch from each edge.
Place a fresh piece of parchment in baking pan, allowing excess to stick out over the edges of pan. Return brownie to pan, top-side up, and set aside.
Meanwhile, working quickly, scoop half of the ice cream into the bowl of an electric mixer fitted with the paddle attachment. Beat the ice cream until soft and smooth but not melted. Using a rubber spatula, transfer the ice cream to brownie pan, and spread, creating an even layer. Place the pan in freezer to chill. Repeat with the remaining 2 pints of ice cream, adding a second layer to the brownie, and return pan to freezer. Let chill until very hard, at least 1 hour (overnight produces the best result).
Fill a medium saucepan halfway with water; bring to a boil. Remove from heat. Place the remaining chocolate and 2 tablespoons butter in metal bowl; set over water. Using metal spoon, stir until melted and smooth.
Remove pan from freezer. Place a cooling rack over a baking sheet, and set aside. Using edges of parchment paper, lift brownie and ice cream out of pan, and transfer to a cutting board. Working quickly and using a sharp hot knife, trim outside edges to even them, wasting as little of the ice cream and brownie as possible. Use hot knife to cut brownie into twelve 2 1/4-by-4 1/4-inch rectangles, and transfer each rectangle to cooling rack.
Remove bowl of chocolate from saucepan, wiping bottom until dry. Fill a 1/2-cup ladle with melted chocolate; carefully ladle chocolate over each bar, working from front to back. Cover as much of the ice cream as you can. Work quickly; do not worry if some ice cream shows. Return rack and baking sheet to freezer. Let stand until chocolate hardens, about 30 minutes. Serve, or store in freezer up to 1 week.
It is best to bake brownies a day in advance so they have time to set completely. Make space in your freezer to accommodate ice-cream bars and baking sheet.