Fill a large pot with water, add 1 tablespoon of salt, and bring to a rolling boil.
Add the pasta and cook according to package directions until al dente, typically 8 to 10 minutes.
While the pasta cooks, place the avocado flesh, basil, garlic, lemon juice, olive oil, salt, and pepper into a high-speed blender or food processor.
Pulse and then blend the sauce ingredients until completely smooth and emulsified.
Just before draining the pasta, carefully scoop out 1/2 cup of the starchy pasta water and set aside.
Drain the pasta in a colander and return it to the warm pot or a large serving bowl.
Pour the avocado sauce over the pasta and toss with tongs to coat thoroughly.
Gradually add the reserved pasta water, one tablespoon at a time, until the sauce reaches a glossy and creamy consistency.
Serve immediately, garnished with halved cherry tomatoes and additional black pepper.