Place chicken livers in a medium saucepan. Cover with water. Add about 1 teaspoon of salt. Boil the chicken livers for 7-10 minutes until cooked through.
Skim foam from the top of the cooking broth, or strain, reserving the broth. Set the livers aside to cool slightly.
Once cool, finely chop the chicken livers or puree in a blender or food processor.
In the meantime, cook ground beef over medium heat until no longer pink, about 7-10 minutes. Use a wooden spoon to break the meat up into bite-sized pieces. Remove the ground beef from the pan and set aside. Reserve some of the grease.
Add the chopped white onion, celery and green bell pepper to the hot grease. Cook until vegetables are tender. Add the minced garlic and sauté for an additional 30 seconds.
Return the ground beef to the pan, along with the pureed chicken livers.
Add the dried thyme and tomatoes with green chilies and stir.
Add the cooked rice and two cups of the reserved stock from the chicken livers. Season with salt and pepper to taste. Nestle the bay leaves in the rice.
Cover the pan and bring to a boil. Lower the heat to low and simmer for 30 minutes.
Garnish with fresh chopped parsley and green onions before serving.