Heat 2 tablespoons of the oil in a 10-inch heavy-bottomed pan or cast-iron skillet. Mix the potatoes with the eggs and flour. Place the potatoes in the pan and distribute evenly over the surface, pressing to form a loose patty. Without moving, cook until the underside is crisp, 4 to 5 minutes. Using a plate, flip and return the hash browns to the pan cooked-side up. Crisp for another 4 to 5 minutes, and then remove from the pan. Cut into quarters and top each quarter with 1/4 cup Pimento Cheese, 2 ounces breakfast sausage, 1 fried egg, and a scattering of scallions to serve.
In a stand mixer fitted with the paddle attachment, add the cheese, mayonnaise, cayenne, garlic powder, onion powder, cream cheese, pimentos and jalapenos if using. Beat on medium speed until combined. Season with salt and pepper.