Preheat oven to 375°. Heat olive oil in a large nonstick skillet over medium heat. Add onion and brown sugar, and sauté 15 minutes or until tender and caramelized. Cool to room temperature.
Combine flour, 2 T sugar, baking powder, and salt in a bowl; make a well in center of mixture. Add onion, cheese, and beer; stir just until moist. Spoon batter into a 9 x 5-inch loaf pan coated with cooking spray; drizzle evenly with butter. Bake for 55-60 minutes, or until a wooden pick inserted in center comes out clean. Cool 5 minutes in pan on a wire rack; remove from pan. Cool completely on wire rack.