In a bowl (or cup), combine double cream, honey, mustard, garlic and a dash of salt. Mix. Set aside.
Season chicken breasts with salt and pepper.
Heat up olive oil on a medium pan (or skillet). Once oil is ready, start browning chicken.
Pre-heat oven to 200°C (375°F).
After browning all the chicken breasts, place them all in the pan. Pour cream sauce on the browned chicken. Add grated parmigiano reggiano on top. Bring to a boil (without covering).
Transfer pan (or skillet) in the preheated oven. After 15 minutes, use a spoon and baste the chicken with some of the cream. Continue cooking for 10-15 more minutes.
Take the pan out of the oven.
Garnish with parsley and more grated parmigiano reggiano.
Serve.