Heat canola oil in a Dutch oven until it reaches 350°F.
Mix potatoes, pork, cheese and cilantro together in a bowl to make the filling.
Roll dough to about 1/8 inch thick on a flat floured surface, and cut out rounds with a 4- or 5-inch cookie cutter. Use fingers to distribute a thin layer of water around the inside edges of the dough circles (this will help to seal the edges). Add filling, fold in half to seal. Use a fork to press edges on both sides to finish seal.
Add sealed empanadas to the hot oil and fry until golden brown, about 3 minutes. Fry in batches.
Serve with sauce(s) of your choice.