Rub the chicken halves all over with salt and pepper.
Place in a covered container and keep in the fridge for a couple of hours.
Heat the cooking oil in a frying pan large enough to accommodate the chicken halves side by side without overcrowding.
Lower the chicken halves in the hot oil, skin side down. Fry over high heat until nicely browned and the skins have puffed, about 7 minutes. Flip to brown the other side.
Lift the chickens with a kitchen spider or tongs and move to a plate. Pour off the oil.
Return the chicken halves to the frying pan. Pour in the mustard cream sauce followed by about half a cup of water.
Stir everything gently but thoroughly.
Bring to a simmer. Cover and braise the chicken halves for about 15 minutes, flipping them over halfway through the cooking time.
Serve the chicken surrounded by the mustard cream sauce.
Optionally, garnish with thinly sliced mint leaves.