Melty Cabbage Pasta Carbonara

Name: Melty Cabbage Pasta Carbonara
Ingredients: 1 ounce Pecorino Romano cheese (about 2/3 cup finely grated or 1/2 cup store-bought grated), plus more for serving; 1 medium green cabbage (about 1 1/2 to 2 pounds); 1 large lemon; 1 tablespoon olive oil; 1 (2- to 3-ounce) can or jar anchovy fillets (do not drain); 2 1/2 teaspoons kosher salt, divided, plus more as needed; 8 ounces dry spaghetti; 4 large eggs; 2 large egg yolks; 1/2 teaspoon coarsely ground black pepper, plus more for serving; 5 sprigs fresh parsley (optional)