Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x5-inch loaf pan.

Whisk beer, 2 tablespoons olive oil, eggs, and salt together in a large bowl.

Mix flour, Parmesan cheese, baking powder, oregano, basil, and thyme together in a separate bowl. Stir into the beer mixture, 1/2 cup at a time, to avoid clumping.

Heat remaining olive oil in a skillet over medium-high heat. Saute onion in the hot oil until translucent, about 5 minutes. Add sausage; cook and stir until slightly browned and crumbly, about 5 minutes. Add garlic and cook for 1 to 2 minutes more. Drain mixture well in a colander, catching the grease in a pan or a bowl. Discard the strained grease and set mixture aside.

Stir sausage mixture, Cheddar cheese, 3 ounces mozzarella cheese, green olives, and black olives into the dough until ingredients are evenly distributed; do not overmix. Pour into the prepared loaf pan.

Bake in the preheated oven for 45 minutes. Sprinkle the remaining mozzarella cheese over the top of the loaf, brush with melted butter, and continue baking until cheese is melted, about 15 minutes; check the bread periodically to be sure cheese doesn't burn during this phase. Transfer bread to a cooling rack until ready to slice and serve.