In small bowl, combine mayo and horseradish.

Form beef into 8 2-oz patties. Make an indent in center of each to prevent burger from puffing up. Season with salt and pepper. Brush with oil. Heat skillet with dollop of oil and butter over medium heat until butter melts. Saute mushrooms until tender. Season with Worcestershire and salt to taste.

Place patties in skillet or on grill and cook for 4 minutes on each side. Turn off heat, top with the cheese and place a lid on the skillet or close the grill. Allow the cheese to melt, about 1 minute.

Heat buns, cut side down, on skillet or grill, for about 1 minute. Assemble the sliders; mayon on bottom bun, Arugula, patty and mushrooms and top of bun.