Whisk together the eggs, milk, 3/4 teaspoon salt and a couple turns of black pepper in a large bowl. Add the potato chips, red peppers, parsley and smoked paprika; stir to combine.
Heat the oil in a medium ovensafe nonstick skillet over medium-high heat. Add the egg mixture and cook until the edges start to set, about 2 minutes. Transfer to the oven and bake until the center is set, 15 to 20 minutes. Let stand for 5 minutes before sliding carefully onto a serving plate and cutting into wedges.