Put a pan of water on to boil for the pasta. Add salt once it starts to boil and bring to the boil again. Cook the pasta according to the directions on the package.
While the water is boiling and the pasta is cooking, beat the eggs with the Parmigiano cheese and a little ground pepper in a bowl.
Heat the olive oil in a frying pan and cook the peeled garlic cloves until they brown. Add the tuna fillet broken into small pieces and cook for a couple of minutes. Remove the garlic cloves.
When the pasta is ready, reserve 1 cup of the cooking water and drain the pasta.
Add the drained pasta to the tuna, mix well and add some pasta cooking water. Cook for a couple of minutes then remove from the heat and add the egg mixture. Stir until the sauce becomes creamy.
If the sauce is too dry, add a little more pasta cooking water and mix until you get a creamy consistency.
Serve immediately with freshly grated pepper, chopped parsley (optional), and more grated Parmigiano.