I have made this bread both with and without cheese, and we prefer it with cheese. I have also used hard cider in place of the beer - gives it a great flavor. Either way, the taste is wonderful! It's hard to wait until it's cool enough to slice. You may eat it hot - just pull chunks off and add some butter.
Preheat oven to 350°F. Grease an 8-inch loaf pan. Or, bake as a round loaf in a 7-inch round casserole dish.
Mix flour and sugar together in a bowl. Pour beer into a separate large bowl; add flour mixture and stir until moistened. Stir in the 2/3 cup of cheese. Pour batter into prepared loaf pan.
Bake until nearly set, 40-50 minutes. Pour melted butter over the top of the bread and top with the 3 tbsp cheese. Continue baking until a toothpick inserted in the center of the loaf comes out clean, about 10 minutes more.
Cool in pan 10 minutes, then remove from pan and place on rack to finish cooling. Slice when cool.