Heat oil in a large heavy skillet. Add potatoes, stir to coat with oil,
then pat into a flat layer. Cook over medium heat until they begin to sizzle
and turn golden around the edges, about 10 minutes.
Stir in the onion and chile and pat into a flat layer again. Cook over medium
heat until the potatoes are browned on the bottom, about 5 minutes.
With a spatula, turn the potatoes over to brown the other side.
If using tomatoes, stir them in and pat into a layer again. Sprinkle with
salt to taste, raise the heat to medium-high, and cook until the potatoes are
nicely browned on the bottom again, about 5 minutes.
If using cheese, sprinkle over the top and cook 2 minutes more, or until
the cheese softens.