Step 1

In a bowl, whisk together flour, yeast, and salt. Make a well in center of mixture; add warm water and 2 tablespoons oil to well. Gradually stir flour mixture into wet mixture to form a ragged dough. Transfer to a floured work surface.

Step 2

Knead with floured hands until dough is tacky but no longer sticky and springs back when pressed with a finger, about 5 minutes. Transfer to a bowl drizzled with oil, turning dough to evenly coat. Cover and let proof at room temperature until doubled in volume, 1 to 1 1/2 hours.

Step 3

Preheat oven to 450°F with a rack in lowest position. Punch down dough, transfer to a lightly floured work surface, and cut in half. Stretch one piece of dough, working outward from center, into an oval, approximately 9 by 13 inches. Brush 2 tablespoons oil onto a rimmed baking sheet. Place dough on sheet; top evenly with mozzarella, leaving a 1-inch border of dough around edges.

Step 4

Stretch second piece of dough on floured work surface to roughly same oval shape. Place over mozzarella, gently pressing to remove excess air from between doughs. Fold edge of bottom dough up and over edge of top dough, pinching to seal edges together. Sprinkle top evenly with Parmigiano; drizzle with remaining 2 tablespoons oil.

Step 5

Stir together garlic, Italian seasoning, parsley, red-pepper flakes, and sesame seeds; sprinkle evenly over dough. Cut several steam vents in top of dough at 2-inch intervals.

Step 6

Bake until dough is golden brown in places and just cooked through, 18 to 20 minutes. (If dough puffs in places while baking, pierce with the tip of a knife to release steam.) Transfer bread from baking sheet to a wire rack and let cool a few minutes. Slice and serve hot, with marinara alongside for dipping.