In a microwave safe bowl add the milk. Now you are going to scald the milk in the microwave. Microwave for 30 secong intervals, stirring after each one, just until steam begins to rise from the milk or it reaches 170 degrees.
In the bowl of a stand mixer (or in a bowl to mix by hand), add the sugar and oil. Pour in the scalded milk and mix. Let the mixture sit for 15 minutes or so until it is warm but not blazing hot. You don't want it hotter than 138 degrees.
Add the 4 cups flour and sprinkle the yeast on top of the flour. Mix until no dry streaks remain. Scrape down the sides of the bowl if needed. The dough will be loose and wet-looking. Cover the bowl and let the sponge rest until puffy and doubled, 45 minutes to 1 hour.
Add the remaining 3/4 cup flour, baking powder, baking soda and salt to the sponge. Mix until the flour is completely incorporated and the dough looks smooth. It may not necessarily clean the sides. Only add additional flour only if it is too sticky to handle or a small piece of dough won't form a ball in your hands. Some doughy residue on your fingers is ok.
Scrape the dough into a lightly greased bowl or container, cover, and let rise until doubled, about an hour.
On a counter sprayed with non-stick cooking spray, roll or pat the dough into about a 18X12-inch rectangle. Spread the softened butter evenly across the dough.
Combine the brown sugar and cinnamon together in a bowl. Sprinkle evenly across the top of the butter. Pat down very lightly.
Starting with one of the long sides and roll the rectangle into a log without pulling and stretching on the dough (but still rolling as tightly as possible). Roll the seam to the bottom. Pat the log into an even thickness.
Cut the log into 12 even pieces. Place on a 13 x 18 sheet pan sprayed with non-stick cooking spray. Cover with lightly greased plastic wrap and let rise until almost doubled, about an hour.
Bake at 350 degrees for 18-25 minutes until lightly golden and baked through. Allow to cool to warm before frosting.
For the frosting, add the cream cheese and butter to a bowl. Whip with a handheld (or stand) mixer until creamy. Add the milk or cream and vanilla. Mix again. Add the powdered sugar and whip until light and creamy.
Spread the slightly warm rolls evenly with the icing. Serve immediately or let cool completely and serve at room temperature. Makes 12 servings.