1. Butter the bread with 1 tablespoon butter and place on a large serving plate.
2. Heat a skillet over medium heat. Fry ham lightly, 3 to 4 minutes. Cover with Gruyere cheese and melt, 1 to 2 minutes more. Set aside and keep warm.
3. Heat remaining butter in another skillet over medium heat. Add egg and cook until white is set, about 3 minutes. Flip carefully and cook until set but the yolk is still runny, 1 minute more.
4. Cover the bread with ham and cheese and top with the egg. Sprinkle with parsley, salt, and pepper.