Place the olive oil in a hot skillet (very large) or pot over medium-high heat. When it shimmers (about 30 seconds), add the onion, pepper and celery. Flatten and allow to cook without stirring for about 2 minutes. Stir in the garlic.
When the vegetables start becoming translucent (about three minutes), add the meats, Rotel, soup and tomato sauce as well as the broth and water. Add the seasonings and allow to simmer about 10 minutes.
Stir in the rice and cook over medium-low heat, covered, until the rice is tender and most of the liquid is absorbed (about 30 minutes).