Make the dough: Sprinkle the yeast over the warm water in a small bowl. Let stand until dissolved. Process the butter and 3 eggs in the work bowl of a food processor until blended. Add the yeast mixture, 3 cups of the flour, and the salt and process until incorporated. With the motor running, continue mixing the dough, adding enough of the remaining flour in small additions to form a stiff dough. Turn the dough out onto a lightly floured surface and knead, adding flour as necessary to prevent sticking, until the dough is smooth and elastic. Cover the dough with a clean kitchen towel and let it rest at room temperature while preparing the filling

Make the filling: in a large bowl, beat the egg until foamy. Add the ricotta and grated cheese and mix well. Stir in the smoked mozzarella and salami.

On a lightly floured surface, roll out the dough to 1/8 inch thick. Cut 3-inch circles from the dough and place 1 tablespoon filling in the center of each circle. Wet the edges of each circle with a pastry brush or the tip of your finger dipped in cool water. Fold half the circle over the filling to make half-moon-shaped turnovers, pressing the edges firmly to seal as you go. Place the pizzette on a kitchen-towel-lines baking sheet as you form them. Reroll the scraps of dough as necessary to use all the filling.

Cover the sheet with a kitchen towel and set the pizzette aside in a warm place until they have puffed slightly, about 20 minutes.

Meanwhile, heat the vegetable oil in a heavy, deep 4-quart pot until a deep frying thermometer registers 350 degrees F. Carefully slip as many of the pizzettes as will float freely into the hot oil. Fry, turning with a wire skimmer as necessary, until golden brown on all sides, about 4 minutes. Remove and drain on paper towels. Repeat with the remaining pizzette, allowing the oil to return to temperature if necessary before adding more pizzette.