Preheat the oven to 350 degrees F.

Place the chicken breast on a parchment paper lined baking sheet and baste with 1/4 stick of the softened butter. Season generously and bake for 30 - 40 minutes, depending on size. When the chicken is cooked through, cut into large chunks.

Peel the carrots and cut them into small cubes. Peel the pearl onions (or, if using frozen, cutoff the stringy ends). In a small saucepan, bring the chicken broth or stock to a boil, then set aside.

In a large casserole melt the remaining butter. Cook the pearl onions for 10 to 15 minutes slowly over a low flame, until they are translucent and caramelized. Add the flour and continue cooking for 2 more minutes, stirring continuously. Add the hot chicken stock/ broth and let simmer for 1 minute until the sauce begins to thicken and lose the taste of flour. Add the half and half, 1/2 teaspoon of salt and 1/2 teaspoon of ground pepper, the chunks of chicken, diced carrots, peas and parsley. Give it a good stir.

Increase the oven temperature to 400 degrees F.

Divide the mixture into 4 mini cocottes or ramekins. Cut 4 circles of puff pastry slightly larger than the mini cocottes. Moisten the edges of the cocottes with the egg yolk mixture. Place one circle on each filled cocotte, pressing down around the edges to seal the pastry circle. Cut a small hole or slit in the center to make a steam vent. Place the cocottes on a rimmed baking sheet to catch any filling that may (will) bubble out.

With a pastry brush, coat the tops with the egg yolk mix. Bake for 15 to 20 minutes or until golden brown.