For the carrot ketchup
Finely slice the carrots, cook them with the brown sugar and vinegar until they reach jam consistency.
Season the duck breast with salt and pepper and sear it on the side of its skin. When cool, vacuumize it and cook it slowly at 65°C for 40 minutes. Let it cool and place on one side. Beat the egg yolks with the oil, truffle cream, salt and pepper. Set aside.
Slice the duck breast and heat the slices on the hot plate. Open the roll and stuff it with the tossed duck, ketchup and truffled mayonnaise.