In a large pot over medium-low heat, whisk together milk, sugar, and oil. Using an instant read thermometer, heat the milk to 120°F. Stir the yeast into the warm milk mixture. Stir in 3 1/2 cups of flour. Take off the heat. Cover the pot with a towel and allow to rest, undisturbed, for 1 hour.
Add the remaining 1 cup of flour, salt, baking powder, and baking soda to the mixture. Stir until combined. Place the lid on the pot and refrigerate the dough until it is completely cool (the dough is easier to handle if it is refrigerated), at least 4 hours or overnight.
Preheat the oven to 375°F. Butter a 9-inch-by-13-inch baking dish, or two 8-inch pie plates or round cake pans.
Remove the dough from the refrigerator. Turn the dough out onto a lightly floured surface. Roll the dough into a large rectangle, about 24x10-inches.
Brush the dough with 4 tablespoons of brown butter (see below). Drizzle 2 cups of the caramel sauce over the dough. Sprinkle the brown sugar and toasted pecans (see below) over the caramel sauce.
Starting at the short side furthest from you, roll the dough toward you, until it resembles a log. Pinch to seal. Turn the dough over so the seal faces the work surface. Slice into 2-inch thick rolls and place in the baking dish cut side down.
Cover the baking dish with a towel and allow to rise for 15 minutes. Place in the oven and bake for 30-35 minutes, or until the rolls are golden brown in color. If rolls are browning too much, lightly cover with foil the last 15 minutes of baking.
Allow the rolls to cool for 10 minutes. Drizzle the remaining caramel sauce over the warm rolls.