In a large pot of boiling salted water, cook the spaghetti until al dente. Drain pasta, reserving about 2 cups of the pasta cooking water.

Bring a large skillet to medium heat. Add olive oil and garlic and sweat for a couple of minutes. Add mussels to the skillet, then add white wine. Cover and cook for 4–6 minutes, or until mussels open. Discard any unopened mussels. Strain the cooked mussels through a sieve to save the broth. Set broth aside.

Return pan to stovetop over medium heat. While the pan is heating, mix egg yolks with 1 cup of the Pecorino cheese to create a thick paste.

Add butter and black pepper to the skillet. Stir for about 1–2 minutes until fragrant. Add reserved mussel broth to the butter/pepper mixture. Bring to a simmer. Slowly whisk in the egg/cheese mixture to create a smooth sauce. (If the sauce is too thick, add some of the reserved pasta cooking water to thin it out. If it’s too thin, add some more cheese.)

Transfer cooked spaghetti and mussels to the skillet with pepper sauce; season with kosher salt. Toss to combine.

Divide pasta and mussels between 4 serving plates and garnish with more grated cheese and a drizzle of extra-virgin olive oil.