In a mixing bowl, combine the beef and minced onions together. Season the mixture with 2 teaspoons of kosher salt, 1 teaspoon of black pepper, and the cayenne. Mix gently to combine, then shape into 16 large meatballs. Insert half of a clove of garlic in the center of each and pinch the beef around it. Combine the flour and Essence in a shallow plate. Roll the meatballs evenly in the flour mixture. Reserve any excess flour.

In a large Dutch oven, heat the oil. When the oil is hot, add the meatballs (in batches if necessary) and brown evenly, using a spoon to turn them. Remove the meatballs from the pan and set aside. Stir in the reserved flour mixture. Stir constantly for 3 to 4 minutes, making a dark brown roux. Add the sliced onions and green peppers. Season lightly with salt and cayenne, and continue cooking until the vegetables are soft, 4 to 6 minutes. Add the broth, bay leaves, and parsley and mix well to combine. Bring to a boil and return the meatballs to the pot. Reduce the heat to a simmer and cook for 1 to 1 1/2 hours, partially covered, until the gravy is thickened and the meatballs are tender. Skim off any fat that has risen to the surface. Remove the bay leaves. Spread one half of each portion of French bread with 1 1/2 tablespoons of the mustard and the other half with 1 1/2 tablespoons of the mayonnaise. Lay two pieces of the cheese on top of the mayonnaise. Place 4 meatballs on each loaf of bread, and top the meatballs with the cheese. Spoon the sauce over the meatballs. Top the meatballs with the remaining half of bread. Cut the sandwich in half and serve immediately.