Cook's Note: To toast the almonds, arrange in a single layer on a baking sheet. Bake in a preheated 350 degrees F oven for 6 to 8 minutes until lightly toasted. Cool completely before using.
Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender but still firm to the bite, stirring occasionally, 8 to 10 minutes. Drain and reserve about 1 cup of the pasta water. Place in a serving bowl.
Using a spoon, scoop out the flesh from the avocados and place in a food processor. Add the arugula, basil, lime juice, garlic, salt, and pepper. Blend until smooth.
Pour the pesto over the pasta and toss together. Add the cheese and almonds and toss together until coated, adding the pasta water, as needed, to loosen the sauce.