Preheat the oven to 375°F. Spray a 9x5-inch loaf pan with nonstick spray.
Heat the oil in a large nonstick skillet over medium heat. Add the onion and sauté 6 minutes or until tender. Cool to room temperature.
Whisk together the flour, sugar, baking powder and salt in a bowl; make a well in the center of the mixture. Add the onion, cheese, and beer. Stir just until moist.
Spoon the batter into the prepared pan. Drizzle evenly with 2 tablespoons of butter. Bake for 35 minutes; brush with the remaining 2 tablespoons of butter. Bake an additional 23 minutes or until a toothpick inserted into the center comes out clean. Cool 5 minutes in pan on a wire rack; remove from the pan. Cool completely on wire rack.