Preheat your oven to 400°F (200°C).

Roll out the chilled puff pastry on a floured surface until it's about 1/4 inch thick. Cut into four squares and place on a parchment-lined baking sheet. Prick the center of each square with a fork and brush the edges with egg wash.

Layer slices of ham on each pastry square and sprinkle generously with Gruyère cheese.

Bake for 10-15 minutes until puffed and golden.

Make a small divot in the center of each pastry, crack an egg into it, and season with salt and pepper.

Return to the oven and bake for an additional 10-15 minutes until the egg whites are set.

Let cool for a minute, garnish with chopped chives, and serve warm.