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 ½ cup of the starchy pasta water. Drain the pasta through a colander and set aside.
02 - While the pasta cooks, place the basil, parsley, chives, tarragon (if using), avocado, Greek yogurt, olive oil, lemon juice, garlic, and Parmesan into a food processor or high-speed blender. Process on high until completely smooth and a vivid green color emerges, scraping down the sides as needed.
03 - Taste the sauce and season with kosher salt, black pepper, and chili flakes if desired. If the sauce is too thick, blend in 2 to 3 tablespoons of the reserved pasta water until it reaches a pourable, creamy consistency.
04 - Transfer the drained pasta to a large mixing bowl. Pour the green goddess sauce over the hot pasta and toss vigorously until every strand or piece is evenly coated. Add additional pasta water, one tablespoon at a time, to achieve a silky, glossy finish.
05 - Divide among serving plates immediately. Garnish with extra torn herbs, an additional sprinkle of Parmesan, and a drizzle of olive oil if desired.