01 - Bring a large pot of generously salted water to a rolling boil. Add the pasta and cook according to package directions until al dente. Before draining, reserve 1/2 cup of the starchy cooking water. Drain the pasta through a colander and set aside.
02 - While the pasta cooks, combine the avocado, spinach, basil, chives, parsley, tarragon (if using), garlic, olive oil, Greek yogurt, lemon juice, Parmesan cheese, salt, pepper, and chili flakes in a food processor or blender. Process on high until completely smooth and the sauce turns a vibrant, uniform green color.
03 - Stop the processor and taste the sauce. Adjust salt, pepper, or lemon juice as needed to balance the flavors. Blend again briefly if any adjustments were made.
04 - Return the drained pasta to the pot or transfer to a large mixing bowl. Pour the green goddess sauce over the hot pasta and toss thoroughly, adding reserved pasta water one tablespoon at a time until the sauce reaches your preferred consistency and coats every strand evenly.
05 - Divide the sauced pasta among individual bowls. Finish each portion with an extra sprinkle of Parmesan cheese, a scattering of freshly chopped herbs, and a light drizzle of olive oil if desired. Serve immediately.