Heat 1 tablespoon of the olive 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 1/2 teaspoons salt, and 1/2 teaspoon pepper and bring to a boil. Add the chickpeas and beans and cook until heated through, about 3 minutes.
Combine the garlic, pine nuts, parsley, the remaining olive oil, 1/4 teaspoon salt, and 1/8 teaspoon pepper in a small bowl.
Divide the chili among individual bowls and top with the pesto. Serve with the bread, if desired.
Shortcut: Instead of chopping the garlic, pine nuts, and parsley by hand, pulse them in a food processor before adding the oil.