Set a large pot of heavily salted water on to boil. Use slightly less water than usual to make the water more concentrated with pasta starch; you need just enough to cover the pasta.

In a mixing bowl, thoroughly whisk together the eggs, both kinds of cheese, a pinch of salt, a generous amount of black pepper, and a splash of cold water.

Boil the pasta in the pot of salted water for 1 minute less than the package's recommendation for 'al dente' noodles.

While the pasta cooks, melt the butter with the garlic cloves in a large skillet over medium heat. Once the butter has melted, allow the smashed garlic to sizzle for a few minutes in order to infuse flavor into the butter. Discard both cloves of garlic.

When the pasta has finished cooking, drain, reserving about 1 cup of pasta water. Toss the pasta in the pan with the garlic-infused butter.

Reduce heat to medium-low; pour in a couple of tablespoons of reserved pasta water and vigorously toss. Dollop in the egg and cheese mixture and continue mixing aggressively until a silky sauce comes together, adding in more pasta water as needed.

Turn off the heat and stir in your parsley. Taste and season accordingly; serve immediately.