Preparation

• Position a rack in the center of the oven and heat the oven to 450°F.
• Spread each slice of bread with about 1 Tbs. mayonnaise and put on a baking sheet. Top each piece with 3 slices of ham and 2 or 3 slices of tomato. Season with salt and pepper. Top with the cheese and bake until the cheese melts and the edges of the bread are light golden-brown, about 10 minutes.
• Meanwhile, melt the butter in a 12-inch nonstick skillet over medium heat until the foam subsides. Crack the eggs into the pan and fry them sunny side up until the whites are set but the yolks are still soft, about 2 minutes. Toss the arugula with the oil and vinegar and season to taste with salt and pepper. Top each sandwich with an egg, season with salt and pepper, and serve with the salad.