Preheat the oven to 350 degrees F.
With a serrated knife, score the bread lengthwise and then crosswise several times making a crosshatch pattern of little squares of bread but keeping the bottom intact and maintaining the shape of the bread.
Using a small rubber spatula, spread the pesto in between the crevices of the bread. Next, wedge the mozzarella slices into the crevices and fill in with the shredded asiago, tucking the cheese into the center of the bread.
Transfer the loaf to a sheet pan lined with foil. Combine the melted butter and garlic and drizzle the mixture evenly over the bread. Season with salt and pepper. Bake until the cheeses are melted and bubbly, about 15 minutes. Serve warm.