Prepare the rice according to package directions, then fluff with a fork, and set aside. Keeping it separate helps the grains stay light instead of softening too much in the pot.
Set a medium pot over medium-high heat and add the olive oil. When the oil is hot, add the carrots, celery, and onion. Cook for 3 minutes, stirring often until softened.
Stir in the garlic, Italian seasoning, and bay leaf. Cook for 30 seconds, just until fragrant.
Pour in the broth and bring it just to a boil. Reduce the heat to low, cover, and simmer for 5 minutes or until the vegetables are fork-tender. Remove the bay leaf and adjust seasoning to taste.
Spoon warm rice into bowls and ladle the soup over the top. Remove the bay leaf, adjust seasoning to taste, and serve hot.