01 - In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, active dry yeast, and salt until evenly combined.
02 - Pour in the warm milk, melted butter, and room-temperature eggs. Mix using a dough hook attachment or wooden spoon until a sticky, cohesive dough forms.
03 - Turn the dough onto a lightly floured surface and knead for 8 to 10 minutes until smooth and elastic. Transfer to a greased bowl, cover with a clean towel, and let rise in a warm spot until doubled in size, approximately 1 hour.
04 - Punch down the risen dough and roll it out on a floured surface into a 16×12-inch rectangle.
05 - Spread the softened butter evenly across the surface of the dough. Sprinkle the packed brown sugar, ground cinnamon, and rainbow sprinkles in an even layer over the butter.
06 - Starting from the long side, roll the dough up tightly into a log. Using a sharp knife or dental floss, slice into 12 equal portions. Arrange the rolls cut-side up in a greased 9×13-inch baking dish.
07 - Cover the dish and let the rolls rise for 30 minutes until puffy. Meanwhile, preheat the oven to 350°F.
08 - Bake the rolls for 22 to 25 minutes until the tops are golden brown and the centers are cooked through.
09 - While the rolls are still warm, whisk together the powdered sugar, milk, and vanilla extract until a thick, pourable glaze forms. Drizzle generously over the rolls and finish with additional rainbow sprinkles. Serve warm.