Preheat oven to 400 degrees. Spray 4 small oven-proof bowls with cooking spray.
In a saucepan over medium heat, melt butter. Stir in 2 cups chicken broth, and whisk in all of the flour, gradually adding the remaining chicken broth until you have a smooth, slightly thick base. Mix in onion flakes, hot pepper sauce, pepper, thyme, bay leaf, and carrots. Cook about 5 minutes. Stir in potatoes and chicken, and cook for another 5 minutes.
In the bottom of each prepared bowl, place a slice of Swiss cheese. Divide the chicken mixture equally into the four bowls, over the cheese. Place a puff pastry square over the top of each bowl, pressing lightly around the rim. Brush the pastry with the egg and water mixture. Place the four bowls on a baking sheet.
Bake until pastry is puffed and golden brown, about 25 minutes. Let rest at least 5 minutes before serving.