Preheat oven to brownie-mix package temperature. Grease a bundt or tube pan well.
Prepare brownie batter per package directions and set aside.
Cut each cinnamon roll into quarters and toss with melted butter.
Combine sugar and cinnamon in a bowl; toss buttered pieces in the mixture until coated.
Layer half the coated pieces into the pan, pour half the brownie batter over them, then repeat.
Bake 25–35 minutes until a toothpick near center comes out with moist crumbs, not raw batter.
Let cool 10 minutes, invert onto serving plate, drizzle reserved icing over top.