In a shallow dish add the flour and lightly coat the chicken breasts. Shake off excess flour and brown in a hot skillet for a minute or two each side. We aren't trying to cook the chicken here, just brown the surface. When they are browned set them aside.
In a bowl add the chopped shallot, Worcestershire sauce, heavy cream, minced garlic, paprika, mushroom powder, salt, and pepper. Add about a half cup of water and mix it up thoroughly.
Place the chicken in a baking dish and pour the cream sauce over it. Put it in the oven at 165 degrees Celsius for 55 minutes. Make sure that you use a small enough baking dish so that when you put the cream sauce over the chicken breasts they are covered.
After the chicken is done use tongs to place the chicken on a plate and put the sauce into a saucepan. On medium heat whisk the sauce around and add a tsp of flour and the butter to thicken it up. Pour it over the chicken breast directly on the plate. Serve the baked chicken cream sauce immediately.