Pour 3 cups of the broth into a large saucepan. Place over high heat and bring liquid to boil. Add rice and bay leaf and give a quick stir. Cover and reduce heat to low and simmer for 30 minutes or until rice is tender and all liquid is absorbed. Remove bay leaf and set aside.
Meanwhile, heat the oil in a large skillet over medium-high heat. Add the garlic, onion, and eggplant. Sauté for 5 to 8 minutes, or until the vegetables soften a bit.
Add the celery, green pepper, tomato, paprika, and thyme. Continue cooking for 5 to 8 minutes longer, stirring occasionally, until the vegetables are soft but not overdone.
Stir in the cooked rice and remaining cup of broth. Reduce heat to medium and cook another 10 minutes until all the liquid is absorbed. The mixture should still be a bit moist, so if need be, add ½ to 1 cup water and allow to absorb a bit.
Stir in salt, pepper, lemon juice and parsley.
Serve at once; pass around Tabasco for spicing up individual servings. Keeps several days in the fridge, flavor improves over time.