Preheat oven to 190 °C (375 °F).
Heat a saucepan over medium heat and add a little olive oil. Sauté the shallots for 1 minute.
Add the bourbon, maple syrup and duck stock to the saucepan. Bring to a boil, and then reduce the heat and simmer on low for 15 to 18 minutes until the liquid has reduced by half.
Pour in the cream and simmer for 3 to 4 minutes or until the sauce has thickened. Remove from the burner and set aside.
Using a knife, make shallow incisions in the skin of the duck breasts in a grid-like pattern, taking care not to cut into the flesh. Season with salt and pepper.
Heat a large ovenproof skillet over low heat. Place the duck breasts in the skillet skin side down. Sear over medium heat for 8 to 10 minutes, without turning the breasts over. If necessary, drain any excess grease from the pan while cooking.
Turn the duck breasts over and continue cooking for 8 to 10 minutes, to an internal temperature of 58 °C (137 °F) (insert a cooking thermometer into the centre of one of the breasts).
Transfer the duck to a plate and cover loosely with a sheet of aluminum foil. Let it rest for 5 minutes.
In the meantime, drain the excess grease from the pan. Deglaze the pan with the reserved sauce and simmer for 3 to 4 minutes over medium-low heat.
Plate the duck breasts, pour the sauce over top and serve.
