In a small heavy saucepan heat 2 tablespoons of the oil over medium heat and whisk in 2 tablespoons flour. Cook, whisking constantly, until roux thickens and darkens to a mahogany color; do not let burn.
When well-colored, add the ground pork and cook, stirring and breaking up pieces, until browned, 4 to 5 minutes.
Add onions, bell pepper and celery and cook, stirring occasionally, until vegetables are tender, 4 minutes.
Add the garlic, 2 teaspoons of the Essence, cayenne, and file powder and cook for 2 minutes.
Meanwhile, in a large pot bring gizzards and 3 cups of water to a boil over high heat. Boil until tender, about 30 minutes; drain, reserving stock and gizzards separately. Grind gizzards in food processor and add to pork and vegetable mixture along with 2 cups of the reserved stock (add water if necessary to bring volume up to 2 cups) and add the salt and pepper. Bring mixture to a boil, then reduce the heat to a simmer. Cook about 30 minutes, until flavors are well-blended.
Add the livers and cook, stirring, until they are cooked through, 2 to 3 minutes.
Add the parsley, green onions and rice, mixing gently but thoroughly to combine.
Adjust seasoning if necessary, transfer to a bowl, and set aside to cool. When cool, cover with plastic wrap and transfer to the refrigerator until thoroughly chilled.
When the mixture is thoroughly chilled, form the mixture into balls about 2 tablespoons each, pressing with your hands to compact the mixture. Transfer to a parchment-lined baking sheet and repeat with remaining mixture.
Place the flour and 4 teaspoons of the Essence in a mixing bowl and toss to combine.
Place the eggs and milk in another shallow mixing bowl and whisk to combine.
Place the bread crumbs in a third bowl, add the remaining 2 tablespoons of Essence and toss to combine.
Working 1 at a time, carefully coat the rice balls first with the flour, then with the egg wash, then dredge in the bread crumbs, rolling to coat evenly and shaking to remove any excess crumbs. Place the breaded boulettes onto a parchment lined baking sheet and repeat with the remaining dirty rice until all boulettes have been breaded.
In a large saucepan heat at least 4 inches of the oil to 350 degrees F. When hot, gently add the boulettes, in batches, to the hot oil, and fry, turning to promote even browning, until golden, about 2 minutes.
Remove from the oil with a slotted spoon and let drain on a paper-lined plate or platter. Season lightly with salt and repeat until all boulettes have been fried.