Heat grill to high. Brush potato halves, onion slices, peppers, and chilies with oil and season with salt and pepper, to taste. Grill potatoes and onions for 2 to 3 minutes per side or until just cooked through and slightly charred. Remove from heat, cut each potato half in half again, and finely chop the onions.
Grill peppers and chilies until charred on all sides. Remove from the grill, place in a bowl, cover and let steam for 5 minutes. Remove skin and finely dice.
Melt butter in a 9-inch cast iron skillet on the grates of the grill. Add the potatoes, onions, peppers and chilies all in 1 layer and pack down. Cook until crisp and nicely browned.