Leftover parottas can be refrigerated.
I've found that the refrigerated parottas when steam cooked (stack the parottas in a glass bowl and cover the bowl with aluminum foil, place it on a deep-bottomed pan with 1 cup water in it, cover the pan with its lid and cook for a few minutes) for few minutes or so makes it soft rather than heating it on the pan or microwaving it.
Tear the leftover parottas into small slices and combine them with chicken roast to make a different dish called "Kothu Parotta" or "Stir fry Parotta".
Here is the recipe for Chili Pita I posted last year, you could make Chili Parotta using this recipe. Add parottas instead of pita.