Coat two or three 9x13-inch baking dishes with the melted butter.
In a medium saucepan over medium heat, add 1 quart of the milk, the vegetable oil, and 1 cup of the granulated sugar and heat to just below a boil.
Transfer the milk mixture to a bowl to cool to room temperature.
Sprinkle the yeast on top of the milk mixture and let it sit, about 1 minute.
Add 8 cups of the flour to the yeast mixture, stir until it is just combined, cover with a clean dish towel, and set aside in a warm place, about 1 hour.
Add the baking powder, the baking soda, 1 tablespoon of the salt, and the remaining flour to the yeast mixture and stir thoroughly to combine.
Place 1/2 of the dough on a flat, lightly floured surface and use a rolling pin to roll the dough into a thin 30x10-inch rectangle.
In a microwave-safe bowl, microwave 1 cup of the butter until it has melted.
Evenly brush the melted butter over the dough.
Sprinkle the remaining granulated sugar and the ground cinnamon over the dough.
Beginning at the longest side of the dough, use both of your hands to tightly roll it towards you, then pinch the seam together and place the dough, seam-side down, on a cutting board.
Use a sharp knife to cut the dough into 1/2-inch slices, making about 20-25 rolls.
Place the rolls in the prepared baking dishes in a row, being careful not to overcrowd.
Repeat the process with the remaining dough, starting with rolling it out and ending with placing the rolls in the prepared baking dishes.
Cover the baking dishes with clean towels and let the rolls rise, about 20 minutes.
Preheat the oven to 375 degrees F.
Bake the rolls until they are golden-brown, about 15-18 minutes, being careful not to over-brown.
While the rolls are baking, in a large bowl, whisk the powdered sugar, the maple flavoring, the remaining milk, the remaining butter, the coffee, and the remaining salt together until the mixture is very smooth and thick, but pourable.
Immediately pour the icing over the tops and edges of the cinnamon rolls.
Plate and serve.