Make the dough first. Combine the flour, eggs, and salt, and knead well until the mixture is firm and elastic; it will be quite firm, and if you can't incorporate all the flour add a little water to the mixture.
Then make the filling. Place the ricotta in a medium mixing bowl and add the scamorza cheese, egg yolks, mint, and prosciutto and mix well. Season the mixture to taste with salt and pepper.
Roll the dough out into a 1/8th in thick sheet – and cut it into 4-inch squares.
Divide the filling up among the squares, setting it in the middle of each, and fold them over the filling, crimping the edges to seal them. Place the oil in a deep fry pan and heat to 350 degrees. Fry the calzoni in hot oil until golden on both sides. Drain them well on absorbent paper, and serve.