Heat the milk, oil, and sugar in a large pot over medium heat until steaming. Do not boil. Cool to 105 to 110°F.
Sprinkle the yeast over the warm mixture and let it sit 5 minutes until foamy.
Stir in 4 cups of flour until combined. Cover and let rise in a warm spot for 1 hour.
Stir in the remaining 1/2 cup flour, baking powder, baking soda, and salt. Bake now or refrigerate overnight.
Roll the dough on a floured surface into a 30 x 10-inch rectangle, about 1/4 inch thick.
Brush with melted butter. Mix the sugar and cinnamon and sprinkle evenly over the butter.
Roll into a tight log from the long side, pinch the seam, and slice into 1 1/2-inch rolls.
Arrange in two buttered 9-inch round pans. Cover and let rise 20 to 30 minutes. Preheat the oven to 375°F.
Bake 15 to 18 minutes until golden brown.
Whisk the powdered sugar, milk, melted butter, coffee, maple flavoring, and salt until smooth. Pour over the warm rolls and serve.