Heat olive oil and butter in a large skillet over medium-high heat. Add mushrooms in a single layer and cook without stirring for 3-4 minutes until browned on one side.

Stir and continue cooking until deeply golden and crispy, about 8-10 minutes total. Add garlic in the last minute. Season with salt and pepper. Set aside.

Cook spaghetti in a large pot of well-salted boiling water until al dente. Reserve 1 cup pasta water before draining.

In a bowl, whisk together whole eggs, egg yolks, grated Pecorino, and black pepper.

Add drained spaghetti to the mushroom skillet (off heat). Pour in the egg mixture and toss vigorously, adding pasta water a splash at a time until a creamy, glossy sauce forms.

Serve immediately with extra Pecorino and black pepper on top.