Warm the water to about 105–115°F (40–46°C). In a small bowl, combine warm water, 1 tablespoon sugar and 2 teaspoons instant dry yeast. Stir and let stand 5–8 minutes until foamy. If it doesn't foam, the yeast may be inactive; start over with fresh yeast.

In the bowl of a stand mixer fitted with the dough hook (or a large mixing bowl), combine 3 cups all-purpose flour and 1 teaspoon salt. Mix briefly to combine.

Add the foamy yeast mixture, 1 cup warm whole milk, 1 large egg and 3 tablespoons softened butter to the flour. Mix on low to incorporate, then increase speed to medium and knead for 6–8 minutes until the dough is smooth, elastic and slightly tacky. If dough is too sticky, add up to 2 tablespoons more flour; if too dry, add 1–2 teaspoons water.

Form dough into a ball, lightly oil the bowl, place dough inside, cover with plastic wrap or a clean towel and let rise in a warm draft-free place until doubled in size, about 60–75 minutes.

Filling

While the dough rises, make the filling. Heat 1 tablespoon olive oil in a large skillet over medium heat. Add the finely chopped onion and cook 4–5 minutes until translucent.

Add 2 minced garlic cloves and cook 30 seconds until fragrant.

Add 1 pound raw sausage (casings removed) to the pan. Break up with a spatula and cook until no pink remains, about 6–8 minutes.

Stir in 2 tablespoons tomato paste, 1 teaspoon dried oregano, 1 teaspoon salt and 1 teaspoon freshly ground black pepper. Cook 1–2 minutes to combine flavors and reduce excess moisture. Taste and adjust seasoning.

Remove the pan from heat and stir in 2 tablespoons chopped fresh parsley and 1 cup grated Parmesan cheese. If using, allow filling to cool slightly before assembly so it doesn’t melt the dough or egg wash.

Assembly & Bake

Preheat oven to 375°F (190°C). Line a baking sheet with parchment paper or lightly grease a 9x13-inch baking pan.

On a lightly floured surface, punch down the risen dough and roll it into a rectangle about 12 x 16 inches, roughly 1/4-inch thick.

If using mozzarella, sprinkle 1 cup grated mozzarella evenly over the dough, leaving a 1/2-inch border along one long edge.

Spread the cooled sausage filling evenly over the cheese (or directly on the dough if not using mozzarella), pressing gently to distribute but leaving the same 1/2-inch border.

Starting from the long edge opposite the border, tightly roll the dough into a log. Pinch the seam and ends to seal.

Using a sharp knife, slice the log into 10–12 equal pieces (about 1 to 1¼-inch thick) for swirls. Place each swirl cut-side up on the prepared baking sheet or arranged in the pan with a small gap between each to allow expansion.

Whisk together 1 egg and 1 tablespoon milk to make an egg wash. Brush the tops of each swirl, then sprinkle with sesame seeds or additional grated Parmesan if desired.

Bake in the preheated 375°F (190°C) oven for 20–25 minutes, or until the swirls are golden brown and the filling is bubbling. If baking in a single 9x13 pan, bake 25–30 minutes.

Remove from oven and let cool 5–10 minutes before serving so the filling sets slightly.