Green Pasta Primavera

Name: Green Pasta Primavera
Ingredients: Kosher salt and freshly ground black pepper; 1 pound your favorite pasta; 1/4 cup extra-virgin olive oil or melted butter, plus more for serving; 4 scallions, thinly sliced; 1 leek, chopped; 2 green garlic stalks, thinly sliced (or 3 garlic cloves, minced); 1/2 broccoli head, chopped; 1 handful green beans, thinly sliced, or green peas; 2 tablespoons freshly squeezed lemon juice, plus more to taste; 2 teaspoons finely grated lemon zest; 2 cups grated Parmesan, plus more for serving; 1 bunch parsley, chopped