Preheat the Oven: Preheat your oven to 375°F (190°C).

Roll out the thawed puff pastry on a lightly floured surface to fit your baking sheet or tart pan. With a knife, slice and transfer the puff pastry to the baking sheet lined with parchment paper. Prick the pastry all over with a fork to prevent it from puffing too much during baking. Line the pastry with parchment paper and fill it with pie weights or dried beans to weigh it down. Bake in the preheated oven for about 15 minutes, or until the pastry is golden.

While the pastry is in the oven, make the béchamel. In a saucepan, melt the butter over medium heat. Once the butter is melted, add the flour and whisk constantly until smooth. Cook for 1-2 minutes, or until the mixture is lightly golden. Warm the milk in a saucepan or in the microwave until hot. Gradually whisk in the milk, ensuring no lumps form. Cook the mixture, whisking constantly, until it thickens and comes to a simmer, about 5-7 minutes.

Remove the saucepan from the heat and stir in the salt, pepper, nutmeg, Dijon mustard, and Gruyere until the cheese is melted and the sauce is smooth. Set aside.

Once the pastry has baked and cooled slightly, remove the parchment paper and weights/beans. Spread the prepared béchamel mixture evenly over the pastry. Arrange the ham and Swiss slices evenly over the béchamel. Carefully crack the eggs, one at a time, into a small bowl, then gently slide them onto the tart, spacing them evenly apart. Spoon a little more of the béchamel mixture over each egg.

Bake for an additional 15-20 minutes until the eggs are cooked and the béchamel is less runny. Rotate the pan halfway through to bake the eggs more evenly. Broil on low for 2 minutes to add some golden-brown crisp to the béchamel.

Once the tart is done broiling, remove it from the oven. Sprinkle chopped parsley over the tart for garnish, if desired. Allow the tart to cool slightly before slicing. Serve warm and enjoy your family-style Croque Madame Tart!