How to Make It
Preheat the oven to 350°. In a roasting pan, rub the chicken with 1 tablespoon of the olive oil and season with salt and pepper. Roast for 1 hour and 30 minutes, or until the juices in the cavity run clear. Let the chicken rest for 10 minutes and increase the oven temperature to 450°. Remove all of the meat from the chicken and discard the skin and bones. Cut the chicken into bite-size pieces.
On a large rimmed baking sheet, toss the oyster mushrooms with 1 tablespoon of the olive oil. Season with salt and pepper. Roast for 8 minutes, or until richly browned. Reduce the oven temperature to 400°.
In a large, deep skillet, melt the butter in the remaining 2 tablespoons of olive oil. Add the carrots, celery, onion, leek and bay leaf. Cover and cook over low heat, stirring occasionally, until the vegetables have softened, about 10 minutes. Stir in the flour, then gradually whisk in the broth until smooth. Simmer over low heat, stirring often, until no floury taste remains, about 5 minutes. Stir in the cream and simmer until thickened, about 8 minutes. Stir in the peas, thyme and chicken and season with salt, pepper and a pinch of smoked paprika. Simmer for 5 minutes.
Line a large rimmed baking sheet with parchment paper. On a lightly floured work surface, roll out the puff pastry to a 1/8-inch thickness. Using a 4-inch round cookie cutter, stamp out 6 rounds; transfer them to the prepared baking sheet. Brush the rounds with the egg-cream wash and bake for 15 minutes, or until puffed and browned. Ladle the chicken stew into bowls, garnish with the pastry and serve.