Coat a rimmed baking sheet with cooking spray or olive oil from a mister. Slice tomatoes and place on baking sheet. Sprinkle with salt (or to taste) and dried basil. Bake for 10-15 minutes.
While the tomatoes are cooking, peel and seed avocados. Combine avocados, lemon juice, sea salt, garlic, edamame, and fresh basil into a food processor. Process until fairly smooth. (The consistency will remain somewhat lumpy even once blended.)
Add avocado edamame sauce to pasta, and mix until the pasta is coated. Top with roasted tomatoes.