Heat a tablespoon of butter in a frying pan over medium heat. Salt and pepper the duck breasts and fry them, skin side first, until the internal temperature reaches 45°C. Remove the breasts from the frying pan, tent with foil, and set aside.
Pour off the fat from the frying pan. Add a tablespoon of butter and the shallots. Cook the shallots for a while without coloring. Deglaze with cognac, ignite, increase heat to high, and reduce totally. Add the stock and mustard. Reduce by about half. Season the sauce with salt and pepper. Finish the sauce with the remaining butter.
Slice the duck breasts on the bias and place on heated serving plates. Spoon the sauce over each portion.