1) Preheat the oven to 180C/Gas 4. Spray four individual-sized baking dishes with cooking spray.
2) Season the chicken with 1/4 teaspoon of salt and a few turns of pepper. In a large nonstick skillet, heat 2 teaspoons of the oil over a medium-high heat. Add the chicken to the pan and cook for 5 minutes, turning once. Transfer the chicken to a plate.
3) Add 2 more teaspoons of the oil, the leeks and the celery to the pan and cook until the vegetables begin to soften, about 3 minutes. Add the potatoes, French beans, garlic and remaining salt and pepper, and cook for 2 more minutes.
4) Add the milk to the pan. In a separate container, stir the flour into the chicken stock until dissolved, then add it to the pan. Cook, stirring, until the mixture comes to a boil. Reduce the heat to medium-low. Cover and simmer, stirring occasionally, for 10 minutes. Stir in the reserved chicken, peas, parsley and thyme. Spoon the mixture into the prepared baking dishes.
5) Put the remaining 2 teaspoons of olive oil into a small bowl. Unroll the filo pastry and cut it into quarters. Place one quarter of the pastry on top of each baking dish and brush with olive oil. Tuck the edges of the pastry into the dish rim. Top each pie with Parmesan cheese.
6) Place the pot pies on a baking sheet and bake until the filling is bubbling, about 30 minutes.