In the bowl of a freestanding mixer, fitted with the dough hook, dissolve 1 tbsp of sugar in the warm water. Sprinkle yeast on top and let sit until foamy, about 10 minutes.
In a small bowl, whisk buttermilk, egg and oil. Pour into the yeast mixture, add the remaining sugar, and stir to combine. Add 2 and 1/2 cups flour until combined, then add the remaining flour. Knead for 5 minutes until the dough pulls away from the bowl and is not sticky to the touch.
Divide the dough into 3 even portions. Working with one portion, add 1-2 tsp of food coloring (depending on color preference) to the dough and knead by hand until the color is incorporated. I lined my countertop with parchment paper so the food coloring would not stain my countertops. Repeat with the second color. Leave one portion of the dough natural.Divide each of the 3 portions of dough into 3 pieces. Place the 9 portions of dough in an oiled bowl, with the colors interspersed, but still touching each other. Cover with plastic wrap, and let proof for 2 hours. Melt butter and set aside. In a small bowl, mix together sugar, brown sugar and cinnamon.
Roll the dough into a rectangle, approximately 12 in by 18 in. Brush with melted butter, leaving 3/4 inch on one of the long sides uncovered. Sprinkle with sugar & cinnamon mixture. Tightly roll the dough, starting with the long side and roll toward the edge with no butter. Pinch seam to seal.
Cut into twelve 1.5 inch rolls using a sharp serrated knife. Place buns in a greased 9 x 13 pan, lined with parchment paper. Cover with plastic wrap and refrigerate overnight.
Fill a glass bowl, or other container, with boiling water and place on the bottom shelf of the oven, put the rolls on the top shelf and let proof 30-45 minutes. Remove the rolls and water from the oven, preheat to 350°F, and bake cinnamon rolls for 30-35 minutes until golden brown.
Let rolls cool while you prepare the frosting. Whip ingredients with a hand mixer or stand mixer until smooth. Spread over cinnamon rolls once slightly cooled. Add sprinkles if desired. Enjoy warm!