Bring chicken broth and bay leaf to a boil in a small pot. Add the rice, cover, and reduce heat to low. Simmer for about 20-25 minutes if using white rice or about 40 minutes if using brown rice, until the broth has been absorbed into the grains. Turn off the heat and fluff the rice with a fork. Return the lid to cover and set aside.
Heat olive oil in a large skillet over medium heat. Add the sliced sausage rounds and cook, stirring occasionally, for 3-4 minutes, until browned on both sides. Use a slotted spoon to remove the sausage to a plate; cover to keep warm.
To the skillet with the rendered sausage fat, add the onion and green pepper and cook, stirring frequently, for about 3 minutes, until tender. Add garlic and stir constantly for 30 seconds, until fragrant. Stir in red beans, diced tomatoes and their juices, salt, black pepper, cayenne, and Creole seasoning.
Add the rice, parsley, and thyme. Cook for about 3 minutes, stirring occasionally, to allow flavors to blend. Return the sausage to the pan and stir to combine. Serve immediately.