Heat a large pan over medium-high heat. Add the oil and the chicken breast. Season with salt and ¼ teaspoon black pepper, and cook for 6-8 minutes, stirring occasionally until the chicken is cooked through.
Transfer the chicken to a medium bowl and return the pan to the stove.
Reduce the heat to medium and melt the butter in the pan.
Add the onion, carrot, and celery, cooking until the vegetables have softened and the onion is translucent, 8-10 minutes.
Sprinkle in the flour, stirring well so there are no lumps.
Add the garlic, parsley and thyme, and cook for 2-3 minutes more, until fragrant.
Pour in the chicken broth and stir occasionally until the sauce has thickened, 3-5 minutes.
Stir in the frozen peas and reserved chicken.
Season with salt and pepper, then pour in the heavy cream.
Stir to combine and cook until the peas have defrosted. Remove the pan from the heat.
Preheat the oven to 375°F (190°C)
Lightly flour a clean work surface. Lay out 1 pie crust and lightly brush the top with water. Place another pie crust on top and lightly dust with flour.
Using a rolling pin, gently roll out the dough in order to bind the 2 crusts, taking care not to make them thinner.
Place a 5-inch (12 cm) metal bowl in the center of the crust and cut out a circle 2 inches (5 cm) larger than the bowl.
Place the cut-out dough circle inside the bowl, making sure to fully press down so the dough is flush against the surface of the bowl.
Fill the bowl with ¼ of the chicken mixture.
Roll the excess pie dough into a large circle. Cover the filled bowl with the dough circle slightly larger than the diameter of the bowl.
Press the edges of the dough together, then use scissors to trim any excess dough. Crimp the edges to close.
Repeat with the remaining pie crusts to make 3 more bowls.
Arrange the bowls on a baking sheet. Use a small knife to make small slits in the top crusts.
Bake for about 45 minutes, until the tops are a deep golden brown.
Let cool until the bowls are cool enough to handle.
To serve, place a plate on top of a pie, then invert onto the plate. Garnish with parsley.