Madame Cristo Sandwich

Combine egg, heavy cream or milk, salt, a pinch of heat from cayenne pepper, a hint of warmness from nutmeg, and the brightness of lemon zest in a bowl. Blend until the mixture is smooth and has a fluid consistency. If necessary, add an extra 2 tablespoons of milk or cream to achieve the desired texture.

Heat slices of bread until they are lightly toasted and have a golden brown color. Add a slice or two of Havarti cheese to each piece of toasted bread. Divide the ham into two equal portions and place one portion on each slice of bread. Bring the two halves together to form a sandwich, then dip it into the egg mixture, coating it evenly. Flip the sandwich several times to ensure it is fully coated and place it on a plate. Repeat with the second sandwich.

In a separate pot, fill it with 2 inches of water and bring it to a rolling boil. Meanwhile, melt butter in a skillet over medium heat. Cook the sandwiches in the hot butter until the outside is golden brown and the cheese is melted, taking about 4 minutes per side.

On the stovetop, reduce the heat to medium-low and pour in vinegar. Keep the water at a gentle simmering temperature. Crack an egg into a small bowl, then carefully slide it into the simmering water, holding the bowl just above the surface of the water. Repeat with the second egg. Cook until the egg white is firm and the yolk has thickened, but not hardened, taking about 2 1/2 to 3 minutes.

Transfer the sandwiches to plates and sprinkle with a pinch of cayenne pepper. Remove the eggs from the water with a slotted spoon, gently pat them dry on a kitchen towel to remove excess moisture, and place them onto each sandwich. Sprinkle with a pinch of cayenne pepper to finish the dish.