Cover the bottom of a large dutch oven or heavy skillet with a half inch of oil. When hot, add the potatoes, stirring to cover in the oil. Moderate the heat so the potatoes don't cook too quickly.
Cook for 8 minutes or so, giving a stir once in awhile. Add the peppers, onions and garlic, stir to mix. Season with the salt, pepper and smoky paprika.
Continue to cook until the peppers and onions have softened and the potatoes are cooked through and have taken on a nice color, about 5 minutes more. It's okay if some are crispier than others.
Garnish with chopped parsley before serving.