In a large bowl, combine the ground beef and onion; season with salt and pepper. Using a food processor, grind the corned beef. Add to the ground beef along with the mustard; mix well with your hands. Form the mixture into twelve 3-inch patties and coat lightly with a drizzle of EVOO (or vegetable oil).
In a medium skillet, heat a liberal drizzle of EVOO (or vegetable oil) over medium-high heat. Add the potatoes, season with salt and pepper and cook for 5 minutes. Stir in the sauerkraut. Add the beer and simmer for 5 minutes.
Heat a large skillet or griddle pan over medium-high heat. Add the patties and cook, turning once, for 6 minutes. Top the burgers with the swiss cheese, cut or folded to fit. Cover loosely with an aluminum foil tent to melt.
Pile the patties on the slider roll bottoms (or the toasts) and top with the potato-kraut. In a small bowl, stir together the sour cream, relish, ketchup and worcestershire. Dollop a generous spoonful of sauce on each slider, then cover with the roll tops (or toasts).