Heat the butter in a large cast-iron skillet over medium-high heat. Add the potatoes, green onions, roasted red pepper, paprika and some salt and pepper; stir and then press everything with a spatula to smash it into an even layer. Cook until it starts to crisp and brown on the bottom, 4 to 5 minutes. Add the burnt ends and use the spatula to fold them into the potatoes, turning everything so that lots of the crispy bits are on top; smash again with the spatula to brown the second side, 4 to 5 minutes more.
Top with the pickled chiles and onions. Sprinkle with the cilantro and serve from the skillet.