Mushrooms: Melt butter in a saute pan over medium heat. Add mushrooms and garlic, cooking until mushrooms lose their moisture and become soft, about 5 minutes.
Whisk Eggs: Whisk together the egg yolks and whole eggs until evenly mixed. Stir in the parmesan.
Pasta: Bring a large pot of water to a boil, then add salt and spaghetti. Cook according to instructions on package, until spaghetti is al dente. When finished, save 1 cup of the water that you cooked the pasta in, and strain out the rest.
Temper Eggs: Very slowly drizzle the 1 cup of pasta water into the eggs, whisking as you pour. This tempers the eggs so that they won't scramble when they hit the hot noodles.
Combine: Stir the egg mixture and mushrooms into the spaghetti noodles. Top with cracked black pepper and more parmesan cheese. Serve immediately.