Preheat the oven to 400 degrees F. Heat the olive oil in a large ovenproof nonstick skillet over medium-high heat. Add the onion and bell peppers, season with salt and pepper and cook, stirring occasionally, until the vegetables start softening, about 5 minutes.
Meanwhile, whisk the eggs with the milk, parsley, 1 teaspoon salt and a few grinds of pepper in a large bowl. Pour into the skillet and stir to combine. Cook until the eggs start setting around the edge, about 1 minute. Transfer the skillet to the oven and bake until set in the middle, about 8 minutes. Top with the cheese, then continue baking until melted, 1 to 2 minutes. Let sit 5 minutes. Meanwhile, toast the rolls on a baking sheet, 3 to 5 minutes.
Cut the eggs crosswise into 4 slices, then cut each slice in half; sandwich between the rolls and top with the pepperoncini. Serve with potato chips.