Boil the gizzards in water to cover in a saucepan over medium heat for about 1 hour, or until tender. Drain, reserving the broth. Finely chop the gizzards in a food processor. Combine the oil and flour in a large heavy saucepan over medium heat. Stirring constantly for 8 to 10 minutes, making a dark brown roux. Add the ground pork to the roux and cook for 5 to 6 minutes, stirring occasionally. Add the onions, bell peppers, and celery and cook for 5 to 6 minutes, or until the vegetables are wilted. Add the chopped gizzards. Pour the reserved broth into a 1 cup measure. Add enough water to make a full cup. Add this to the pot.
Mix in the cooked rice, stirring to coat evenly and break up any clumps. Add the salt, cayenne, green onions, and parsley. Mix well. Cook until the rice is warmed through, stirring occasionally. Season the entire chicken with Essence. Stuff the quail in the chicken. Stuff the dirty rice into the cavity of the chicken, around the quail. Reserve the remaining dirty rice