Zucchini Carbonara

Name: Zucchini Carbonara
Prep time: 20 min
Cook time: 20 min
Total time: 40 min
Cuisine: European, Italian, Mediterranean
Ingredients: 2 large eggs; 4 large egg yolks; 1/2 cup freshly grated Parmigiano Reggiano cheese, plus more to garnish; 3/4 cup freshly grated Pecorino Romano cheese; 1 teaspoon coarsely ground black pepper; 1/2 teaspoon kosher salt, plus a pinch; 3 large zucchinis (about 1 1/2 pounds); 2 tablespoons olive oil, such as Fratepietro; 2 cloves garlic, smashed and peeled; 1/4 cup basil leaves, torn; 1 pound long pasta, such as Spaghetti Chitarra or Bucatini