Butter one side of each bread slice and place on a serving dish. Top each slice with 2 ham slices.
Arrange lettuce leaves on the plate next to the bread. Cut the cucumbers into fan shapes and place them next to the lettuce along with the tomato quarters.
Heat 25 g butter in a large skillet over medium heat for about 2 minutes until foaming. Crack both eggs into the skillet, reduce heat to low, and fry for 4-5 minutes until the whites are set and opaque but the yolks remain liquid. Season with salt and pepper.
Carefully transfer the fried eggs onto the bread slices and sprinkle with chopped parsley.