Ham and Cheese Pan Souffle

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

Kosher salt

6 large eggs, at room temperature, separated

8 ounces manchego or aged provolone cheese, grated (2 cups)

1 tablespoon all-purpose flour

Freshly ground pepper

4 tablespoons extra-virgin olive oil, plus more if needed

1 onion, halved and thinly sliced

2 Anaheim chile peppers, halved, seeded and thinly sliced

1/4 pound boiled ham, cut into small cubes

1 teaspoon paprika

2 tablespoons chopped fresh parsley

1 clove garlic, minced