Cook the chicken:
Place the chicken breasts in a pot with enough water to cover them. Boil for 15 minutes, then remove from the heat and leave the chicken in the broth for 10 more minutes.
Reserve ½ cup of the broth. Store the rest in the fridge or freezer for future use.
Finely chop the chicken into small pieces.

Sauté the vegetables:
Heat the olive oil in a wide pot over high heat. Add the mushrooms and sauté for 2–3 minutes, until all their liquid evaporates.
Add the onion, garlic, and carrot. Cook for 3 minutes, until the onion becomes translucent.

Make the creamy filling:
Sprinkle the flour over the vegetables and cook for 1 minute, stirring constantly. Add the nutmeg.
Pour in the broth and milk, stirring continuously. Add the chopped chicken, season with salt and pepper, and simmer until the mixture thickens into a creamy sauce.
Remove from heat and let cool for 10 minutes, stirring occasionally.
Add the grated cheese and mix well. The filling should be thick, not runny.

Assemble the pastry roll:
Unroll the puff pastry onto a baking sheet lined with parchment paper.
Place the cooled filling in a long strip down the center of the pastry.
Fold the sides over and roll tightly into a log, keeping the seam underneath.
Score the top lightly and brush with the egg yolk mixed with a little water.

Bake:
Bake in a preheated oven at 200°C (392°F) for 10 minutes.
Reduce heat to 170°C (338°F) and bake for another 30 minutes, until beautifully golden.
Let rest for 10–15 minutes before slicing and serving.