Preheat oven to 350 degrees F (175 degrees C). Grease and flour 2 9-inch cake pans.
Combine the brownie mix, vegetable oil, water, and eggs in a mixing bowl; stir well with a spoon until thickened and smooth, about 1 minute. Spread the batter into the prepared cake pans.
Bake in the preheated oven until set and browned, about 30 minutes. A toothpick inserted into the center of a pan should come out with moist crumbs. Let cool for 10 minutes in pans before removing to finish cooling on racks.
After brownies are cool, remove ice cream from freezer and allow to soften for about 10 minutes. Meanwhile, pour sweetened condensed milk into a saucepan, and mix in the chocolate chips; heat over low heat, stirring constantly, just until chips have melted and the sauce is smooth. Remove from heat and allow to cool to barely warm temperature.
Place one of the layers of brownies into the bottom of a 9-inch springform pan. Evenly spread the ice cream in a layer over the brownies; pour and spread half the chocolate sauce over the ice cream. Top with the other brownie layer, and drizzle the remaining sauce over the top. Freeze until ready to eat, at least 1 hour. Serve topped with whipped topping, if desired.