01 -
Bring a large pot of salted water to a boil. Cook the spaghetti until al dente, then reserve 1 cup of pasta water before draining.
02 -
In a medium bowl, whisk the egg yolks, whole egg, heavy cream, Parmesan, black pepper, and 1/4 teaspoon salt until smooth.
03 -
Heat olive oil in a large skillet over medium heat. Add the diced ham and cook for 4-5 minutes, stirring often, until the edges are lightly browned.
04 -
Stir in the minced garlic and cook for 30 seconds, just until fragrant. Do not let it brown.
05 -
Add the hot drained spaghetti to the skillet with the ham and toss well. Remove the skillet from the heat.
06 -
Pour in the egg and Parmesan mixture while tossing constantly. Add reserved pasta water a few tablespoons at a time until the sauce is glossy and coats the noodles.
07 -
Taste and adjust with salt and more black pepper. Serve immediately with extra Parmesan and parsley if using.