Ham and Cheese Pan Souffle

potatoes, peeled and cut into 1/2-inch cubes

salt

extra-virgin olive oil, plus more if needed

onions, halved and thinly sliced

Anaheim chili peppers, halved, seeded and thinly sliced

boiled ham, cut into small cubes

paprika

chopped fresh parsley

garlic, minced

large eggs, at room temperature, separated

cheddar cheese

all-purpose flour

freshly ground black pepper