Cook the pasta in a pot of salted boiling water for 9-11 minutes, reserving 1/2 cup of starchy pasta water before draining.

Sauté the sliced mushrooms in olive oil for about 3 minutes until browned, then add minced garlic and cook for another minute.

In a bowl, whisk together egg yolks and Parmesan cheese until smooth.

Combine the sautéed mushrooms with the drained spaghetti, add the egg mixture and reserved pasta water, tossing to combine.

Adjust the sauce consistency with more reserved pasta water as needed, and stir in chopped parsley, salt, and pepper.

Serve warm, garnished with additional Parmesan and crushed red pepper flakes, drizzled with olive oil.