1. Brush 1 tablespoon of melted butter over the bottom and sides of an 8 by 8 by 2-inch baking dish.
2. Mix the brown sugar, sugar, cinnamon, and cloves in a small bowl.
3. Roll out the thawed dough on a lightly floured surface to a 12 by 9-inch rectangle. Brush 1 tablespoon of butter over the dough. Sprinkle the sugar mixture over the dough, leaving a 1/2-inch border along the bottom side. Starting at the top, roll up the dough jelly-roll style, forming a log. Pinch the seam to seal. Cut the log into 9 equal pieces. Arrange the rolls, cut side down, in the prepared baking dish, spacing evenly.
4. Cover the dish with plastic wrap. Let the rolls rise in a warm draft-free area until puffed, about 45 minutes.
5. Position the rack in the center of the oven and preheat to 325 degrees F.
6. Bake the cinnamon rolls uncovered until the tops are golden brown, about 25 minutes. Meanwhile, whisk the powdered sugar, cream cheese, and half and half in a medium bowl until smooth and creamy.
7. Brush the remaining 1 tablespoon of butter over the baked cinnamon rolls and then drizzle the cheese mixture over top. Serve warm.