Cook the onions, bell pepper, celery, and garlic in two tbsp of the oil in a Dutch oven, about 3-4 minutes.
Add shrimp and cook until shrimp are pink, about 5 minutes.
Remove shrimp mixture and reserve.
Add last tbsp oil to the pan along with the rice and cook over med-high heat about ten minutes, until the rice is a light brown, stirring frequently to prevent scorching.
Stir in the broth, tomatoes, salt, pepper, thyme, Tabasco, and the bay leaf.
Heat mixture to a boil then cover, reduce hear and simmer, about 15-20 minutes or until rice is tender.