Preheat oven to 375°.
Heat olive oil in a large nonstick skillet over medium heat. Add onion, and sauté 6 minutes or until tender. Cool to room temperature.
Lightly spoon flour into dry measuring cups, and level with a knife. Combine flour, 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 2 tablespoons butter. Bake at 375° for 35 minutes; brush with remaining 2 tablespoons butter. Bake an additional 23 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.