Diamond score the bread: Preheat oven to 375°F (190°C). Using a sharp serrated bread knife, slice the bread boule diagonally in 1-inch intervals, cutting about 3/4 of the way down without cutting through the bottom crust. Turn the loaf 90 degrees and slice diagonally again in 1-inch intervals to create an accordion-style diamond crosshatch pattern.

Make garlic herb butter: In a small bowl, whisk together melted butter, olive oil, minced garlic, chopped parsley, salt, and red pepper flakes.

Stuff with cheese: In a mixing bowl, toss shredded mozzarella and fontina cheeses together. Place the scored bread on a large sheet of heavy-duty aluminum foil. Gently separate the bread cubes with your fingers and stuff the cheese blend generously deep into every single cut and crevice.

Drench with garlic butter: Use a silicone pastry brush (or spoon) to generously drizzle the garlic herb butter mixture down into all the crevices and all over the crusty top cubes. Shower the top with grated Parmigiano-Reggiano cheese.

Bake covered, then crisp: Loosely wrap the aluminum foil up and over the loaf to seal it. Bake at 375°F (190°C) for 15 minutes to melt the interior cheese completely. Open the foil, exposing the top of the bread, and bake uncovered for 8 to 10 more minutes until the crust is deeply golden, crispy, and the cheese is bubbling.

Serve hot: Transfer to a wooden serving board immediately. Serve piping hot with a bowl of warm marinara dipping sauce, allowing guests to pull apart the cheesy cubes!