Cut the mozzarella into small cubes and place them in a medium-sized bowl. If the mozzarella is runny, leave it in a colander to drain excess liquid for 30 minutes. Then pat it dry with a paper towel before placing it in the bowl.
Add the tomato puree to the mozzarella and mix them together until the cheese is fully coated. Now, add the salt and oregano to taste and set the mixture in the fridge.
Dough preparation:
Dissolve the yeast in a little lukewarm water in a large bowl and then add the sugar.
Add the flour to the yeast mixture.
In a separate small bowl, mix about 1½ cups of lukewarm water together with the coarse salt until it has dissolved.
Pour the salty water over the flour and mix all the ingredients together. You can add more water if necessary to get an even consistency, but be sure it is not too sticky. If the dough is sticky, add more flour. Now, add the oil and knead the dough until it is smooth and soft.
Divide the dough into 10 pieces and form small balls. Then place them on a cutting board and cover them with a clean kitchen towel. Now, let the balls of dough rest for about 2 hours so that they can rise and double in size.
Form the panzerotti:
With a rolling pin, roll out the balls of dough into circles and then place a spoonful of filling in the center. Be careful not to overfill them or the filling will come out when you try to close them.
Fold each panzerotto in half to create a half-moon shape. Then seal the edges tightly by pinching them lightly between your fingers or gently pressing them with a fork. You can also dip your finger in a bit of water and run it along the edge to help seal it.
Frying Instructions:
Heat a generous amount of sunflower oil over medium-high heat in a large frying pan. Make sure you have enough space and oil in the pan to deep fry the panzerotti.
When the oil is hot, carefully place the panzerotti into the pan and fry them on each side for 1 to 2 minutes. When they are golden and crisp, take them out and set them aside to drain on a paper towel-lined plate. You will most likely need to do this step in a few batches.
Baking instructions:
Preheat the oven to 230°C/ 450°F.
Place the already formed panzerotti on a baking sheet lined with parchment paper or a silicone baking mat.
In a small bowl, mix a small amount of tomato puree, olive oil, and salt.
Spread a spoonful of the tomato mixture over each panzerotto.
Bake them in the oven for 10-15 minutes or until golden.