Heat the vegetable oil over medium-high heat in a large skillet and brown the sausage, 5 to 6 minutes. Add the onions, bell peppers, celery, salt, Essence, cayenne, and black pepper. Cook, stirring often, until the vegetables are wilted, 10 to 12 minutes. Add the garlic and cook for 2 to 3 minutes. Dissolve the flour in the water and add to the meat mixture. Stir until the mixture thickens slightly, about 3 minutes. Remove from the heat and add the green onions and rice. Mix well and let cool. Stir in the cheese.
Sift the flour, salt, and baking powder into a mixing bowl. Cut in the shortening unit it resembles coarse meal. In a small bowl, beat the egg with the milk. Gradually add the egg mixture to the flour mixture, working it to make a thick dough. Divide the dough into 12 equal portions. On a lightly floured surface, roll the dough pieces into thin rounds, about 5 inches in diameter. Put about 1/4 cup of the mixture in the center of each round, fold over and crimp the edges with a fork. Heat the shortening a deep pot or an electric deep-fryer to 360 degrees F. Fry the pies, two to three at a time, until golden brown. Drain on paper towels and serve immediately.
Combine all ingredients thoroughly.