Heat 1 tablespoon of the oil in a large saucepan over medium-high heat. Add the onion and carrots and cook until tender, about 5 minutes.
Stir in the tomatoes and their liquid, 2 cups water, 1 ½ teaspoons salt, and ½ teaspoon pepper and bring to a boil.
Add the chickpeas and cannellini and kidney beans and cook until heated through, about 3 minutes.
Combine the garlic, pine nuts, parsley, remaining ¼ cup oil, ¼ teaspoon salt, and ⅛ teaspoon pepper in a small bowl.
Divide the chili among individual bowls and top with the pesto. Serve with the bread, if desired.