Preheat the oven according to the brownie mix instructions. Line the bottom of a straight-sided 9-inch square baking pan with parchment paper that overhangs 2 sides.
Line the bottom of the pan with 16 saltines. Combine the brownie mix, eggs, oil and 1/4 cup water in a large bowl and mix well. Pour over the crackers. Bake according to the package directions, or about 35 minutes. Let cool completely.
Soften the ice cream to spreading consistency and pour over the brownie layer; spread evenly. Place 16 crackers on top of the ice cream and freeze at least 4 hours or up to overnight. Remove from the pan using the parchment overhang and cut into 16 pieces with a chef's knife, placing the knife between the saltine crackers.