Heat 1 tablespoon of the oil in a large, heavy pot or Dutch oven over medium-high heat. Add the sausage and cook, stirring to break the meat up, until all pink has disappeared, 5 to 6 minutes. Transfer the sausage to a plate lined with paper towels to drain.
Season the chicken pieces with the salt. Add the remaining tablespoon of oil to the pot. Add the chicken and brown evenly on all sides. Remove the pan from the heat and carefully drain off any excess oil that has accumulated in the pot.
Add the sausage, rice, tomatoes, broth and TABASCO® Sauce. (If using the garlic-flavored oil, add here.) Bring to a boil, then reduce the heat to medium-low, cover the pot and simmer until the rice is tender and most of the liquid has been absorbed, about 25 minutes.
Remove from the heat and let stand, covered, for 10 minutes.
Serve warm from the pot.
For the garlic oil: Heat the vegetable oil in a small skillet over medium heat. Add the garlic and cook, stirring occasionally, until the garlic is very brown. Strain and use according to taste.
Makes 6 to 8 servings.