Add 1 tablespoon avocado oil to large pot and heat pot on stovetop over medium-high heat. Swirl or tilt pot occasionally to distribute oil across entire surface and heat until oil is hot and shimmery.
When oil is ready, add 1 medium onion and 2-3 cloves garlic. Stir to incorporate then sauté 3 minutes or until onions and garlic have softened.
Add 2 cups chopped bell pepper, 2 cups chopped zucchini, and 2 cups chopped eggplant. Stir to incorporate, then cook 5 minutes, stirring occasionally.
After 5 minutes, add 1 28-ounce can tomatoes, 1 28-ounce carton vegetable stock, 1 teaspoon salt, 2 teaspoons dried basil, and 1 teaspoon dried parsley. Stir gently to incorporate ingredients then bring mixture to boil.
Once boiling, immediately reduce heat under pot to medium-low. Simmer uncovered 20 minutes or until vegetables have softened.
Once vegetables have softened, ladle approximately 50% of soup into traditional blender. Set blender aside and let soup cool 3 to 5 minutes, then carefully blend mixture until completely smooth. See Notes for tips on how to safely blend hot liquids.
Return blended mixture to pot and stir to reincorporate. Taste soup and season with additional salt and/or freshly cracked black pepper if desired.
Ladle prepared soup into serving bowls. Top each serving with pesto to taste, ½ tablespoon chiffonaded basil leaves, and shaved fresh parmesan if desired. Serve immediately with pieces of baguettes.