In a large pot of boiling salted water, cook the pasta according to
package instructions. Reserve 100 ml of water.
Whisk together eggs, half of the Parmesan and half of the Pecorino.
Add about 50 ml of the reserved pasta water and a pinch of salt and
pepper. Mix the rest of the Parmesan and Pecorino in another bowl.
Heat the butter in a large skillet over medium high heat. Add the
whole clove of garlic and Guanciale. Cook until brown and crispy,
remove the garlic.
Remove the skillet from the stove and stir in the spaghetti. Add the
egg and cheese mixture while stirring. Add the rest of the cheese and
stir until completely incorporated. Add the reserved pasta water,
until the desired creamy consistency is reached.