Mash the eggs with a fork or place in a food processor and pulse once or twice. Transfer to a medium bowl, add butter and mayonnaise. Stir well with a fork to blend the ingredients. Season well with salt and pepper. Spread 4 slices of bread with a thin layer of mayonnaise.
Spread the remaining 4 slices with good amount of egg filling, top with the mayonnaise slices and press gently.
Remove crust and cut each sandwich 2 into triangles. Serve with French Fries.