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
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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.
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Add the cherry tomatoes and olives to the pan and cook until the tomatoes soften, about 3 minutes.
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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.
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Transfer the scallions to a collander and allow the juice to drain into a bowl. Cool to room temperature. Discard the juice.