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Ingredients

1. 6 ounces sliced boiled ham, coarsely chopped
2. 1/4 cup mayonnaise
3. 1 tablespoon Dijon mustard
4. 1 teaspoon hot sauce
5. 1/4 teaspoon cayenne pepper
6. 2 tablespoons snipped chives
7. Four 3/4-inch thick slices of firm white sandwich bread
8. 1 tablespoons plus 2 teaspoons unsalted butter, softened
9. 1 tablespoon extra-virgin olive oil
10. 4 large eggs
11. Kosher salt and freshly ground black pepper

Directions

1. In a food processor, pulse the ham until finely chopped. Transfer the ham to a bowl and stir in the mayonnaise, mustard, hot sauce, cayenne and chives.
2. Toast the bread until golden. Spread the toast with 2 teaspoons of the butter and top with the deviled ham.
3. In a very large nonstick skillet, melt the remaining 1 tablespoon of butter in the olive oil. Crack the eggs into the skillet and cook over moderately high heat until the whites are set, about 2 minutes. Season each egg lightly with salt and black pepper. Using a spatula, set the eggs on the deviled ham sandwiches and serve immediately.