Heat oil in a small skillet over medium-low heat. Add onion to pan; cook 10 minutes or until browned, stirring occasionally. Stir in pepper and garlic; cook 1 minute.
Add flour, sugar, baking powder, and salt in a large bowl and stir until well mixed. Using the back of the spoon make a well in center of mixture. Add onion mixture, cheese, and beer to flour mixture, stirring just until moist.
Spoon batter into a 9 x 5–inch loaf pan coated with cooking spray. Drizzle 1 Tbsp butter over batter. Bake at 375℉ for 35 minutes. Drizzle remaining 1 Tbsp butter over batter. Bake an additional 25 minutes or until deep golden brown and a wooden pick inserted into the center comes out clean. Cool in pan 5 minutes on a wire rack; remove from pan.