Heat 1 tablespoon olive oil in a large pot over medium heat. Add onion, carrots, and celery. Cook until softened, about 5 minutes.
Add garlic, zucchini, and yellow squash. Cook for another 5 minutes.
Stir in diced tomatoes, vegetable broth, thyme, oregano, salt, and pepper. Bring to a boil, then reduce heat and simmer for 20 minutes.
While the soup is simmering, make the basil sauce. In a blender, combine basil leaves, pine nuts, nutritional yeast, olive oil, and lemon juice. Blend until smooth.
Serve the soup hot, drizzled with basil sauce.