Combine equal parts of plain bread crumbs and flour in a small bowl. Dip the alligator meat in the flour mixture and set the pieces aside. In a large skillet, heat the oil over medium-high heat. Add the alligator meat to the hot oil and pan-fry until all sides are evenly browned. When the alligator is cooked through, remove the meat with tongs, and drain the excess oil on a paper towel-lined plate. Immediately add salt and freshly ground pepper to taste. Before serving, squeeze the juice of 1 lemon on top of the fried alligator.
In a food processor, pulse the garlic, green onion, and white onion until minced and thoroughly combined. Add the egg yolks and lemon juice, and pulse again until blended. Slowly drizzle the oil into through the feeding tube of the processor until the sauce emulsifies. When the sauce is thickened, add salt, pepper, and a couple drops of hot pepper sauce, to taste. Serve as a dipping sauce for the Fried Alligator.
Combine the olive oil and butter in a large skillet over medium-high heat. When hot, add the onion and shallot to the pan, and saute for 2 to 3 minutes. Add the garlic, and then add the alligator meat. Saute the alligator for 8 to 10 minutes, or until the meat begins to brown, flipping the meat when the first side begins browning. Add the tomatoes, parsley, lemon juice, and olives to the pan. Bring to a simmer, and then lower heat to maintain a simmer for 35 to 40 minutes. Add salt and pepper, to taste.
Pound the alligator with a meat mallet to tenderize. Heat a large skillet over medium-high heat, and then add the olive oil and 4 tablespoons of butter. Add the shallot, and saute for 4 to 5 minutes, stirring with a wooden spoon so that it doesn't burn. Add the alligator meat to the pan, and saute for an additional 8 to 10 minutes, or until the alligator browns slightly. Add chicken stock and flour, and then cook for 2 to 3 minutes, or until the sauce thickens. Lower the heat to medium-low, and add the capers and lemon juice, and then simmer for 15 minutes. Add butter, as needed, to thicken the sauce. Garnish the plate with lemon wedges.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.