In a small bowl, stir together the cherries, balsamico and sugar. Cover and place in the refrigerator for at least 30 minutes.
Heat up the olive oil in a non-stick pan on medium/low heat with a pinch of salt and add the minced shallot. Cook for a few minutes until the shallots turn transparent and then add the cherries, including all balsamico and cherry juice in the bowl. Simmer on medium-low heat, stirring periodically, until the liquids have reduced to a thick syrup and the cherries are very soft, approximately 15 minutes.
Score the fat on top of the duck breast diagonally in two directions. Cut all the way through the fat without cutting into the meat. Season generously with salt and pepper.
Heat a sauté pan over medium-low heat and then place the duck in the pan, fat-side down. Allow the fat to render until it's dark brown and crisp, approximately 10 minutes. Drain some of the duck fat from the pan periodically to avoid splatter.
Flip the breast and allow it to cook on the opposite side for a few minutes, until an instant read thermometer reaches 125 degrees F in the center of the breast. Allow the meat to rest for at least 5 minutes.
While the duck is resting, prepare the foie gras. Heat up a nonstick skillet on high until it's very hot. Lightly score one side of the foie gras and season with salt and pepper. Place the foie gras into the hot skillet, which should immediately start sizzling (if it doesn't remove the foie and allow the pan to continue to get hot). Sear for approximately 45 seconds per side.
Lay a bed of arugula on two plates.
Slice duck on the bias into thin strips and fan it over the arugula. Add one slice of foie gras to each plate, scored side up, and serve immediately.