Place flour in a wide bowl, making a well in the center of the flour. Add two of the egg yolks to the well and begin beating the yolks with a fork, drawing the flour into the yolks a little at a time. Add the last egg yolk and continue processing the mixture. Add half of the balsamic vinegar and process for a minute more. When the dough begins to hold together and the eggs are completely absorbed into the flour, it is ready to be kneaded.
Transfer the dough to a lightly floured surface and work the dough until it forms a ball. Knead for 5 minutes. You may have to add a little more flour to the dough if it starts to stick to your hands or work surface. Form dough into a ball and drizzle remaining balsamic vinegar over. Cover with a damp cloth and let rest for 10 minutes. Divide the dough into 2 pieces.
Working with one dough ball at a time, roll into a square, about 1/16th of an inch thick. Allow the dough to rest for 10 minutes while you make the stuffing. Cut the square in half with a knife.