Carefully cut a pocket into the side of the duck breast horizontally, being careful not to cut all the way through. Combine the goat cheese and walnuts in a bowl, then gently spoon inside the pocket in the duck breast. Set aside.
Macerate the dried cherries in 1 cup of the Champagne for 10 minutes. Pour the rest of the Champagne in a saucepan and simmer until reduced to 1/4 cup. Stir in sugar, season to taste and set aside.
Cut a crosshatch pattern into the skin of the duck breast being careful to not cut through to the flesh. Sprinkle the flesh side with salt.
Place in the oil in a pan, skin-side down, over medium-low heat. Cook to render of some of the fat and crisp up the skin, 5 to 7 minutes.
Flip the breast, reduce the heat to medium and cook on the flesh side, about 4 minutes for medium-rare. Remove from the pan and allow to rest for 5 minutes.
Slice and serve topped with sauce and mashed sweet potatoes.
Mashed Sweet Potatoes with Goat Cheese:
Peel the sweet potatoes and cut into 1/2-inch pieces. Place the potatoes in a large saucepan, fill with water to cover and add some salt. Bring the water to a boil over medium-high heat. Cook the potatoes until fork tender (a fork pierces a piece easily), about 13 minutes.
Drain the potatoes well. Transfer them to a food processor and blend until smooth. Add the goat cheese, butter, honey, cinnamon, ginger and 1/2 teaspoon salt. Blend again until everything is well combined. Transfer to a bowl and let cool for 1 minute.
Spoon the potatoes into a resealable plastic bag with its corner snipped or a pastry bag fitted with a tip, or spoon directly onto plates.