Step 1

Place 3/4 cup plus 2 tablespoons warm water in the bowl of a stand mixer (or large bowl if kneading by hand). Sprinkle with 1 tablespoon granulated sugar and 1 packet active or instant dry yeast, stir to combine, and let sit until foamy, about 5 minutes.

Step 2

Add 2 tablespoons olive oil and stir to combine. Add 2 1/2 cups all-purpose flour and 2 teaspoons kosher salt. Mix with the dough hook attachment on the lowest speed until a mostly smooth dough forms that doesn’t not stick to the sides of the bowl, 6 to 7 minutes. (If kneading by hand, stir the dough together until shaggy, then transfer to a work surface and knead by hand until smooth, about 3 minutes.)

Step 3

Remove the dough from the bowl and lightly coat the bowl with olive oil. Return the dough to the bowl. Cover the bowl with plastic wrap or a kitchen towel and let rise in a warm place until puffed and increased in bulk by about 1 1/2 times, 1 to 1 1/2 hours. Meanwhile, make the filling.

Step 4

Drain and pat 8 ounces fresh mozzarella cheese dry with a paper towel. Cut into small dice (about 1 1/2 cups). Place in a medium bowl, add 1/2 cup tomato passata or purée, 3/4 teaspoon dried oregano, and 1/2 teaspoon kosher salt, and stir to combine. Divide the filling into 8 portions (2 slightly heaping tablespoons each) and place on a large plate. Refrigerate until ready to assemble.

Step 5

Line a baking sheet with parchment paper. Gently punch down the dough and divide into 8 (2 1/2 to 3-ounce) portions. Working with 1 piece at a time, roll the dough in tight circles against an unfloured work surface while pressing slightly down. When you feel the dough start to tighten and smooth out, continue rolling it in a circular motion, but slowly lift your fingers to form a cage around the dough with your fingertips brushing the work surface. When a fairly smooth ball forms, stop and place the ball on the baking sheet. Loosely cover the dough balls with plastic wrap.

Step 6

Lightly flour a work surface and rolling pin or dowel. Working with one dough ball at a time, roll and stretch it into a 6-inch round about 1/8-inch thick. Place one portion of the filling onto the center of the round and flatten slightly. Fold each round in half, making sure the top half completely covers the bottom half and pressing out as much air as possible.

Step 7

Press down to seal the edges together. Pick up the panzerotto and roll the rounded edge under itself by about 1/4 inch. Place back on the work surface and seal the rounded edge further by pressing down with the tines of a fork. Return to the baking sheet, keeping the dough balls and panzerotti under the plastic wrap at all times. Start heating the oil when you have filled half the panzerotti.

Step 8

Heat 3 cups canola oil in a Dutch oven or 10-inch high-sided skillet over medium-high heat until 350ºF. Fit a wire rack over a second baking sheet. Fry the panzerotti in batches of 2: Add to the hot oil and fry until golden brown, flipping once, 1 1/2 to 2 minutes per side. Use a spider or slotted spoon to transfer to the wire rack. Let cool 5 minutes before serving.