Roast Beef Sliders with Caramelized Onions

oil

large yellow onions, thinly sliced (about 4 cups)

mayonnaise

prepared horseradish

package (12 oz) 12-count dinner rolls (not pulled apart)

deli roast beef (about 12 slices)

slices baby Swiss cheese (about 3 oz)

butter, melted

finely chopped fresh parsley