Preheat oven to 425F. Chop chicken into bite sized pieces and remove any visible fat. Bring the chicken stock to a boil and place in chicken and carrots. Simmer for 15 min.
Meanwhile in a large saucepan melt the butter and cook the celery and onion. Add the thyme, salt and pepper. Cook until the celery is soft and the onions are translucent. Stir in the flour and let cook for 1-2 min. Don't brown. Slowly add the milk and whisk well. When the chicken is done add the frozen peas and stir to defrost and reheat slightly. Add some of the broth to loosen up the flour mixture and then slowly incorporate the rest of the chicken, peas and carrots, stirring well not to get lumps. Simmer over low heat until thickened stirring occasionally. Adjust seasoning if necessary.
Place the chicken mixture into four baking dishes or ramekins. Roll out puff pastry to 1/8" and cut out ovals or circles to fit just inside your baking dish. Place on top of your baking dishes and brush with a light coating of the half and half cream and sprinkle with paprika.
Place dishes on a rimmed baking sheet and bake for 35-40 min. until the pastry is lightly browned and the filling is bubbling. Let cool for 5-10 min. before serving.
Nutrition calculation is an estimation only. If you need nutritional calculations for medical reasons, please use a source that you trust.