Makes 4 sandwiches
Preheat oven to 400 degrees and line a baking sheet with foil or parchment paper for easier cleanup.
Melt butter in a small pan and combine with garlic, salt, lemon juice, and parsley.
Cut bread in half, and slice horizontally to make four sections. Using your fingers, gently scoop and discard some of the soft inner part of the thickest bread, leaving a one-inch-thick shell. Brush shells with garlic butter and place them on prepared baking sheet.
Heat olive oil in a medium skillet over medium heat. Add sausage and cook, stirring as needed, until browned and fat is rendered, about 8 minutes. Remove sausage from pan with a slotted spoon to drain; set aside.
Divide sauce evenly among bread pieces and spread with a spoon. Divide mozzarella and fontina evenly among over sauce. Top with sausage, then thyme, red-pepper flakes, and Parmesan, if desired. Place bread in the oven and bake for 8 to 10 minutes until hot and bubbly. Serve immediately, drizzled with extra virgin olive oil, if desired.