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Put the chopped avocado, lemon zest, lemon juice, almonds, garlic and half the basil into a food processor. Blend on high until smooth or the texture you prefer. Put the blended sauce in the refrigerator to store if you are not using it right away.  When zesting the lemon, avoid getting the white rind in the zest. It will make the sauce too sour. Lemon is a strong flavor. You might want to start with half the recommended amount and see if it is enough. You can always add more if you want more lemon flavor. Put the dry or fresh spaghetti into a large pot of salted, boiling water. Follow the directions on the package. About 2 minutes before you think the spaghetti is done, taste a couple of strands. Continue tasting every 2 minutes until it reaches your desired texture. Remove the pasta from the boiling water with a slotted spoon or pour it into a colander to drain. Put the drained pasta into a serving bowl. Pour the avocado sauce over the spaghetti and toss to make sure the noodles are coated well. Then sprinkle the basil leaves and parmesan on the spaghetti before it is served to add color and flavor.
Blend the sauce ingredients. Boil the spaghetti. Drain the spaghetti. Add the sauce.