For the béchamel sauce:

1. In a small saucepan, melt the butter. Once the butter has melted, add the flour, whisk until combined, and cook for just a couple of minutes.
2. Continue whisking and slowly drizzle in the milk, and cook until the sauce has thickened. Off the heat, add a pinch of salt, a pinch of nutmeg, and the Dijon mustard.

For the croque madame:

1. Preheat oven to 400 degrees.
2. Line a baking sheet with parchment paper.
3. On a lightly floured work surface, roll out the puff pastry dough and cut it into four equal pieces. Place the dough pieces onto the parchment paper-lined baking sheets and score a 1/2″ border on each piece. 
4. Spread a small amount of béchamel sauce on each piece of dough. Top the béchamel sauce with the grated cheese.
5. Cut each piece of ham in half. Using the ham, create a small well around the sauce and cheese, and use the back of a spoon to tamp down the cheese, creating room for the egg. Add a few pinches of thyme on top of the cheese.
6. Crack an egg into each well that you created. Depending on the size of your eggs, you may need to remove some of the egg whites before you add them to the puff pastry so the eggs fit into the wells. 
7. Top the eggs with a little salt and pepper, and brush the exposed puff pastry crust with the egg yolk mixture.
8. Place the baking sheet in the oven and bake for about 18 minutes, rotating the pan halfway through to ensure they bake evenly.
9. Remove from the oven, top each piece with fresh chives, plate, and serve immediately.