Add 1/2 cup butter in a saucepan, swirling, until butter foams and starts to turn brown and smells nutty. Remove from the heat and set aside to cool. In a small bowl, mix together the sugar and cinnamon.
Shape the balls. Punch the dough down and divide and roll into small balls, about 1 to 1 1/4 inch in diameter. If you want to be precise about it, each ball should weigh about 15 grams.
Dip the balls into the brown butter and roll in the cinnamon sugar mix. Place each coated ball into a lightly buttered bundt pan, repeating until you finish all of the dough. Cover the bundt pan with plastic wrap and let rise for 20 minutes.
Heat the oven to 350°F.
Optional: While the oven is warming up, mix the leftover brown butter with 2-4 extra tablespoons of melted butter, 1/4 cup brown sugar, and 1/2 tsp vanilla. Just before you put the monkey bread into the oven, pour the brown butter syrup evenly into the bundt pan.
Bake for 35-45 minutes or until golden brown and cooked through. Cover with foil if the top starts browning too quickly. Cool for 5-10 minutes, then very carefully invert onto a large plate.
