Remove bread and wipe skillet clean, then add more butter to fry Eggland’s Best eggs. Fry two eggs at a time, as not to overcrowd pan. Cook the eggs for 4-5 minutes each, until white is set but yolks are still runny. Remove cooked eggs and set aside, then fry the other eggs.
Make aioli by mixing all ingredients together and season with salt. Spread aioli on both sides of bread.
Place a fried tomato on the bottom slice of bread. Spread a generous amount of pimento cheese atop each fried tomato, top with 2 lettuce leaves and place the Eggland’s Best fried egg atop that.
Season the egg yolk with a pinch of salt, and serve with the top bun tilted against the sandwich to show off that beautiful fried egg. Enjoy!