In a mixing bowl, combine beef, salt, pepper and grated onion. Place corned beef in a food processor and pulse to grind it up. Add to the beef along with mustard and mix well with your hand. Form 12 small 3-inch patties and coat them lightly with a drizzle of oil.
Meanwhile, heat a liberal drizzle of EVOO or vegetable oil in a medium skillet over medium to medium-high heat. Add potatoes, season with salt and pepper and cook 5-6 minutes. Add sauerkraut and stir. Add beer and simmer 5 minutes more.
Heat a large skillet or griddle pan over medium-high heat. Cook patties 3 minutes on each side. Cut or fold the Swiss cheese slices to fit the burgers and melt over burgers under a tin foil tent.