Score the duck skin in a crosshatch pattern with a sharp knife. Season the duck breast generously on both sides with salt and pepper.
Heat the olive oil in a pan over medium-high heat (375°F/190°C). Place the duck breast skin-side down and sear for 6-7 minutes until the skin is crispy.
Flip the duck breast and cook for 3-4 minutes more for medium-rare. Remove from pan and let rest under foil to keep warm.
In the same pan with the duck fat, sauté the shallots and garlic for 1 minute until fragrant.
Add the dried cherries, pecan pieces, and demi-glace. Reduce heat to low and simmer gently for 2-3 minutes.
Stir in the fresh mint and season with salt and pepper to taste.
Slice the duck breast evenly and arrange on a plate. Pour the sauce over and serve.