Bring a large pot of salted water to a boil over high heat. Add the pasta and cook according to package directions until al dente. Drain and reserve about ½ cup of the pasta water.
Place avocado, arugula, basil, ¼ cup toasted almonds, lemon, garlic, sea salt and ¼ cup grated parmesan cheese in the bowl of a food processor (or in a blender). Process until totally smooth.
Toss together cooked pasta and avocado pesto in the pasta pot or in a large serving dish. Add pasta water a tablespoon at a time, if needed, to help loosen the sauce.