Grind the short rib and skirt steak. Mix the ground meat with no spices or seasoning. Form into balls.
In a heated skillet on medium-high heat, melt 4 tablespoons of clarified butter and toast your brioche bun. Remove and set aside. Place your meat on the hot skillet and flatten with a burger press. Sprinkle a pinch of salt and pepper on the patty in the pan. Cook on first side until browned and turn to cook the second side to the doneness desired.
Assemble the burger with the toasted brioche, cheese, caramelized onions, and sauce au poivre. (Recipe for the sauce and caramelized onion follows below.)
Deglaze the skillet used to cook the burger. Heat 2 tablespoons of clarified butter and cook over moderate heat, stirring occasionally until lightly browned. Add the brandy and cook, stirring occasionally until reduced by half. (Alternatively, you can flambee the brandy in the pan to burn off the alcohol.)
Add the cream, 2 tablespoons of butter, freshly ground pepper, and brined green peppercorns. Simmer until the sauce is slightly thickened.
Cut onion into slices about ½ inch thick and separate the layers. Heat ¼ cup grapeseed oil in a medium pot and add the onions. Stir often. Turn the heat to medium and cover and cook for 5 minutes. Deglaze with water as needed and scrape the fond from the bottom of the pot. Add a pinch of salt, stir, and return the cover.