Drizzle the olive oil into a heavy Dutch oven or pot set over medium heat. Add the chicken and cook until browned. Using a slotted spoon, remove from the Dutch oven to a plate.
Add the onions, potatoes and carrots and cook until the onions are translucent and the potatoes and carrots are slightly tender, about 8 minutes. Add the butter and allow to melt. Then, stir in the flour, salt and pepper and cook until thickened, about 2 more minutes. Pour in the chicken stock and bring to a boil. Add back in the chicken and their juices.
Ladle the chicken pot pie filling into a 3-quart casserole dish or individual dishes set on a parchment or foil lined baking sheet. Top with puff pastry. Trim the edges of the puff pastry to about 1/2-inch overhang of the rim of the baking dish. Using a sharp knife, cut a slit in the puff pastry as a vent to allow steam to escape during baking. Bake until golden brown and the pot pie is bubbling, about 30 minutes.
Substitute rotisserie chicken or leftover chicken for the uncooked chicken called for ingredients. Omit from the instructions in step 2 and simply shred and add into the pot pie at the end of step 3 in the instructions. Cook the chicken pot pie until the puff pastry is golden brown and flaky.
This can be made into individual servings. Simply ladle the chicken pot pie filling into six individual oven-safe containers.