Preheat oven to 375°F (190°C). Line a rimmed baking sheet with parchment paper or a large sheet of heavy-duty aluminum foil.

Using a sharp serrated bread knife, slice the sourdough boule diagonally in 1-inch intervals, cutting deep into the loaf but stopping about 1/2 inch before the bottom crust to keep the base intact. Turn the loaf 90 degrees and slice in 1-inch intervals in the opposite direction to create a diamond cross-hatch pattern.

In a small heatproof bowl, combine melted butter, minced garlic, chopped parsley, dried oregano, salt, and crushed red pepper flakes. Whisk vigorously until fragrant.

Using a silicone pastry brush and your fingers, gently pry open each crevice of the loaf and generously brush the garlic herb butter deep inside all cuts, reserving about 2 tablespoons for the top.

Toss shredded mozzarella and grated parmesan together in a bowl. Gently stuff generous pinches of cheese into every cut and crevice of the bread until packed to the brim.

Brush the remaining 2 tablespoons of garlic herb butter over the top crust. Wrap the entire loaf loosely in aluminum foil to seal in moisture.

Bake covered for 15 minutes to melt the cheese through the center. Carefully unwrap the top foil and bake uncovered for an additional 10 to 12 minutes until the crust turns deeply golden and the cheese bubbles with toasted peaks.

Remove from oven, garnish with a sprinkle of fresh parsley and flaky salt, and serve immediately warm with warm marinara dipping sauce.