Warm the oil in a large saucepan over medium heat. Add the onion, carrot, and celery, and cook until the vegetables are just tender, 4 to 5 minutes. Add the broth and bring it to a boil over high heat.
Add the tortellini, and cook until they float, 3 to 5 minutes. Stir in the pesto, ladle the pasta into shallow soup bowls, and serve it with the bread.
Tip: Have a rind of Parmesan lingering in your cheese drawer? Toss it into the soup for deep, rich flavor.