Place hamburger, onion, garlic, Creole seasoning and salt in frying pan on medium heat; break up hamburger as it browns. Retain 2 tablespoons of fat in the pan; discard any excess.
Add diced celery and bell pepper to pan and sauté until vegetables have softened.
Add white rice, stirring frequently, until the rice is opaque; ~3 minutes.
Stir in beef and chicken broth; bring to a bubbly boil; reduce heat to low, cover, simmer ~25 minutes.