To make the dough:
- In the bowl of a stand mixer fitted with the dough hook attachment, combine the olive oil, yeast, and water. Let stand until the yeast is dissolved, 5-8 minutes.
- In another mixing bowl, whisl together the flour and salt. With the mixer running on low speed, slowly add the flour to the yeast mixture. Mix until a smooth, supple dough forms, 8 to 10 minutes.
- Transfer the dough to a bowl brushed with olive oil. Brush the ball of dough with more oil. Cover with plastic wrap and set aside to rise for 1 hour, or until doubled in size.
- Transfer the dough to a floured work surface and knead for 2 to 3 minutes. Cut the dough into six 2-ouunce (56 gr) pieces. Roll each piece into a 1/2 inch (6 mm) thick round. (Don't worry if it isn't perfectly round: you will adjust the shape later with a ravioli cutter.)
To make the mozzarella filling:
- Add 2 tablesponns (14 gr) of mozzarella to the center of each piece of dough. Follow with 1 tablespoon (8 gr) of Parmigiano Reggiano and 1 tablespoon (10 gr) of diced tomatoes. Add 4 or 5 capers, if using. Season with black pepper and fold the dough over to create a pocket.
- Seal the edges around the filling by pressing with your fingers. You can also seal them with the floured tines of a fork. With a ravioli cutter, trim the edges, leaving a border about 1 inch (13 mm) wide. Add any scraps from the edges to a ball to make other panzerotti. Lay the panzerotti on a floured baking sheet and cover with a dish towel until they're ready to be fried.
- Heat 1 inch (2.5 cm) of frying oil in a 5-quart (4.7 L) heavy-bottomed stockpot over medium-high heat. Fry the panzerotti in batches until golden brown, about 2 minutes per batch.
To make the Scallion Filling
Put a large saute pan with a lid over a medium flame and heat the oil. add the anchovies and red pepper flakes to the pan. Cook until the anchovies break down. About 30 seconds.
Add the cherry tomatoes and olives to the pan and cook until the tomatoes soften, about 3 minutes.
add the scallions and wine to the pan and cook until the scallions begin to soften, about 5 minutes. Lower the flame slightly. Cook covered for 20 minutes, or until the scallions are tender. Taste for seasoning and add salt as desired.
Transfer the scallions to a collander and allow the juice to drain into a bowl. Cool to room temperature. Discard the juice.