Pour 3 cups of water or broth into a large pot. 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 (brown rice may need an additional 10 minutes) or until rice is tender and all liquid is absorbed. Remove bay leaf and set aside.
May be done a day or two ahead and stored well-covered in refrigerator. Bring to room temperature before proceeding.
Heat oil in a large skillet over medium-high heat. Add chopped garlic, onion and eggplant. Saute, stirring for 5 minutes, or until vegetables soften. Add chopped celery, green pepper, tomato, paprika and thyme. Continue cooking another 5 to 8 minutes, stirring occasionally. Stir in rice and remaining 2 cups of water or broth.
Reduce heat to medium and cook another 10 minutes until mixture is moist but all liquid is absorbed.
Stir in salt, pepper, lemon juice and chopped parsley, and for a pop of protein and bright green color, fold in optional edamame.
Serves 6 to 8. Keeps several days in the fridge, flavor improves over time.