Melt the butter in a large (10 to 12-inch) saute pan. Add the potatoes, onions, salt, and pepper and cook over medium-low heat for 15 to 20 minutes, turning occasionally with a flat spatula, until the potatoes are evenly browned and cooked through. (Allow the potatoes to cook for 5 minutes before turning.) Turn off the heat and add the parsley, scallions and ham. Reheat on top of the stove or over a hot charcoal grill.
Cook's Note: Use any leftover potatoes in Potato Basil Frittata (see recipe) for lunch.
You can peel and dice the potatoes early and keep them in the refrigerator in a bowl of cold water. Drain them and dry them well with paper towels before frying.