Preheat oven to 350°F. Line an 8×8 or 9×9 pan with foil (leave an overhang on opposite sides to lift the brownies later) and spray the foil with cooking spray.
In a medium bowl, stir together ½ cup vegetable oil, 1 cup granulated sugar, ⅔ cup unsweetened cocoa powder, 2 large eggs, 1 teaspoon vanilla extract, and 1 tablespoon water until smooth.
Stir in ½ cup all-purpose flour until combined, then stir in 1 cup chocolate chips. Spread the batter evenly in the prepared pan.
Bake for 23–26 minutes, until the top just starts to lose its glossy sheen. (They can be slightly underbaked if you prefer a fudgier texture.)
Remove from oven and let the brownies cool completely in the pan.
In a separate bowl, stir together ¼ cup sweetened condensed milk, 2 tablespoons peanut butter, ¼ teaspoon vanilla extract, and 1½ cups whipped topping (or fresh whipped cream) until evenly combined. Stir in ¾ cup chopped peanut butter cups.
Use the foil overhang to lift the cooled brownie slab out of the pan. Empty and clean the same pan, then line it with plastic wrap, making sure the plastic overhangs the edges and comes up the sides.
Remove the foil from the brownie slab and place the slab back into the lined pan on top of the plastic. Spread the peanut-butter/ice-cream-style mixture evenly over the top of the brownie slab. Wrap the plastic wrap up over the top to completely cover the ice cream layer (add more plastic wrap as needed).
Freeze the assembled brownies for at least 4 hours or overnight. Store the finished brownies in the freezer.
Notes
You may use a box mix or my homemade brownie mix for an 8×8 or 9×9 pan if you prefer.