Preheat oven to 375°F. Spray the mini-Bundt cake pan with nonstick spray. Set aside.
When the dough cycle finishes, cut the dough in half. Use half of the dough for the mini-king cakes and the other half for another purpose, like rolls.
Roll the retained half of the dough on a floured surface to approximately 13 inches by 17 ounces. Trim to a neat rectangle that is 12 inches by 16 inches.
Brush the dough with the melted butter and sprinkle on the sugar/cinnamon mixture.
Using a pizza cutter or sharp knife, cut four 4-inch-wide strips width-wise from the dough. Then cut each of the strips into three 4-inch-wide strips. You will have a total of 12 strips that are 4 inches by 4 inches.
Cut each dough strip in half (2 inches by 4 inches). You will now have 24 rectangles, 2 inches by 4 inches.
Roll each of the 2 x 4-inch rectangles, jelly-roll fashion, into little logs. Bring the ends together and pinch the dough to seal the seam. Place in the prepared mini-Bundt pan and press down slightly. Cover and let rise in a warm place for 20 to 30 minutes.
Bake in a preheated 375°F oven for 14 to 15 minutes or until golden brown. Remove from oven and allow to cool slightly.
Dip each Bite-Sized King Cake in the frosting, allowing the excess to drip off. Sprinkle on purple, green, and yellow sprinkles.
Yield: 24 Bite-Sized King Cakes.