Combine 2 cups flour, sugar, dry yeast and salt in a large mixer bowl and stir until blended. Combine milk and butter in a microwave-safe bowl. Microwave on HIGH in 15 second increments until very warm but not hot to the touch (120° to 130°F. Butter won’t melt completely). Add to flour mixture with egg.
Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add 1 cup flour; beat 2 minutes at high speed, scraping bowl occasionally. Stir in just enough remaining flour and 1/4 cup rainbow sprinkles so that the dough will form into a ball.
Knead on lightly floured surface until smooth and elastic and dough springs back when lightly pressed with 2 fingers, about 6 to 8 minutes. Cover with a towel; let rest for 10 minutes.
Cut dough into 36 pieces. Combine melted butter and vanilla. Dip half of the dough pieces into the melted butter and place in fluted tube pan that has been generously sprayed with cooking spray. Sprinkle with half the sugar; repeat with remaining dough and sugar. Drizzle any remaining butter over dough. Cover with towel; let rise in warm place until doubled in size, about 45 to 60 minutes.
Bake in preheated 375°F oven for 25 to 30 minutes or until golden brown. Cool 5 minutes in pan, then invert on serving plate.
Combine cream cheese, butter, powdered sugar, vanilla and milk in a medium bowl. Beat with an electric mixer until creamy. Spread over rolls. Sprinkle with 1 tablespoon sprinkles.