Step 1

In a stand mixer with the dough hook, mix the flour, sugar, salt and yeast on medium until well combined, about 15 seconds. With the mixer on low, drizzle in the oil followed by the water. Scrape the sides of the bowl. Mix on medium, occasionally scraping the sides of the bowl as well as the hook, until the mixture forms a cohesive, slightly sticky dough that clears the sides of the bowl, 4 to 6 minutes; the dough will not be completely smooth. Using a silicone spatula, scrape the sides of the bowl and gather the dough in the center. Cover with plastic wrap and let rise at room temperature until doubled, 1½ to 2 hours.

Step 2

Meanwhile, in a small bowl, stir together the roasted peppers, onion, capers, parsley, pepper flakes and vinegar; set aside.

Step 3

About 30 minutes before you are ready to shape and fill the dough, heat the oven to 450°F with a rack in the middle position. Mist a 13-by-18-inch rimmed baking sheet with cooking spray, then line it with kitchen parchment. Mist the parchment, then dust with flour.

Step 4

When the dough has doubled, turn it onto the prepared baking sheet. With the long edge of the baking sheet nearest you, use lightly oiled hands to press and stretch it into an even layer that covers the surface of the baking sheet; it’s fine if the dough doesn’t completely fill the corners. Using a large slotted spoon, spread the roasted pepper mixture in an even layer over the dough, leaving a 2-inch border at the top and a 1-inch border on each short side; discard any liquid remaining in the bowl. Lay the salami slices over the pepper mixture, overlapping them to fit. Layer on the provolone slices, then sprinkle evenly with the mozzarella.

Step 5

Lift up the edge of the parchment closest to you and use it to help fold about 1 inch of the dough over the filling. Continue to roll the dough, without the parchment, until you reach the far edge. Pinch the seam to seal, then pinch the open ends (do not fold them under). Roll the stromboli seam side down and carefully reposition it diagonally on the baking sheet, making sure the seam remains on the bottom. Brush the top and sides with beaten egg and sprinkle evenly with Parmesan. Using a sharp paring knife, cut 5 or 6 shallow diagonal slashes, evenly spaced, into the top so the filling is visible.

Step 6

Bake until well browned and some of the cheese is bubbling through the slashes, 25 to 30 minutes. Using a wide metal spatula, transfer the stromboli to a cutting board and cool for 15 minutes. Use a serrated knife to cut into slices.

Step 7

Spicy Tomato-Basil Sauce: In a medium saucepan over medium, combine 1 tablespoon extra-virgin olive oil and 1 medium garlic clove (minced). Cook, stirring occasionally, until the garlic just begins to brown, 1 to 2 minutes. Stir in ½ teaspoon red pepper flakes, followed by one 14½-ounce can whole peeled tomatoes (crushed by hand) with juices, ¼ teaspoon white sugar and ¼ teaspoon each kosher salt and ground black pepper. Bring to a simmer and cook, uncovered and stirring occasionally, until the sauce is lightly thickened, 8 to 10 minutes. Off heat, stir in 2 tablespoons finely chopped fresh basil. Taste and season with salt and black pepper.