In a small bowl, stir together the flour, baking powder, granulated sugar, milk, vanilla extract, and melted butter until a soft dough forms.
Turn the dough out onto a clean, lightly floured surface. Gently press and shape it into a small rectangle, approximately 4 inches by 6 inches.
In a separate small bowl, combine the melted butter, brown sugar, and cinnamon. Stir to form a thick paste.
Spread the filling evenly over the dough rectangle, leaving a small border around the edges.
Starting at one of the short ends, gently roll the dough into a cinnamon roll shape.
Spray the inside of a standard microwave-safe mug (mine was an 8-ounce mug) with nonstick spray or grease with butter. Place the roll in the mug, spiral side facing up.
Microwave on high for 90 seconds. If the dough still looks wet on top, microwave in 10-second increments until it looks dry and springy to the touch. A toothpick inserted in the center should come out with a few moist crumbs, but no wet batter.
Drizzle warm caramel sauce over the roll and serve immediately.