Using a 3-inch round biscuit/cookie cutter, cut 15-18 rounds from the tortillas. Gently press the tortilla rounds into the cups of a mini muffin tin. Bake at 400°F for 8 minutes. Remove from tin and cool.
Peel and quarter potatoes, then boil until just tender. Drain and cool completely. Chop cooled potatoes into small chunks. A shortcut method is to thaw frozen hashbrowns instead.
Add chopped Capicolla Toppers to a skillet over medium heat. Fry for 2-3 minutes. Add oil and onions to the pan, and saute until onions are soft and translucent. Add garlic and saute for 1 minute. Add potatoes, and cook until heated through. Mix in cheese until melted. Season with salt and pepper to taste.
Arrange the tortilla cups on a baking sheet. Fill each tortilla cup with Capicolla and potato mixture. Top with more shredded cheese. Bake at 350°F for 10-15 minutes, or until the cheese has melted and cups are heated through.