Lemon Garlic Pasta

25min · 6 servings 16 oz fettuccine pasta ¼ cup extra-virgin olive oil 5 cloves garlic, minced ¼ tsp red pepper flakes ½ cup heavy whipping cream 2 tbsp butter 1 tbsp lemon zest ¼ cup lemon juice ½ cup parmesan cheese, grated; plus more for garnish ⅓ cup starchy pasta water, reserved from cooking pasta (before draining) salt and pepper, to taste fresh parsley, chopped; for garnish