Place a large pot on the stove over medium-low heat, and add the olive oil and 1 tablespoon of the butter.
When the butter is melted and foamy, add the chicken pieces and season to taste with salt, pepper, and garlic powder.
Saute the chicken until golden brown, then remove from the pot with a slotted spoon and set aside.
Add the carrots, potato, celery, onion, bay leaves, and thyme to the pot and season to taste with salt, pepper, and garlic powder.
Saute the vegetables until the onions become translucent, then add the remaining 3 tablespoons of butter.
When the butter has melted, sprinkle the flour on top and stir the mixture until all the vegetables are coated in flour.
Deglaze the pot with the white wine, scraping the bottom with a spoon to bring any browned bits up into the sauce.
Stir in the chicken stock and cream, and bring the mixture to a simmer.
Stir in the peas, corn, and reserved chicken pieces.
Allow the filling to simmer until the potatoes and carrots are fork tender. (If it becomes too thick, add more stock until you reach the desired consistency.)
Taste, adjust seasoning as needed, and ladle the filling into bowls. Set aside and allow to cool slightly.
Preheat the oven to 400 degrees F, roll the puff pastry out to a thickness of 1/8-inch, and cut into squares that are slightly larger than your serving bowls. Refrigerate.
When the oven has come up to temperature, lay a square of pastry over each bowl, and cut vents in the top to allow steam to escape.
Bake for 40 to 50 minutes, or until the pastry is puffed and golden brown.