Heat the oil in a saucepan over medium-high heat. Cook the mustard seeds and shallots until the shallots are translucent. Add the beets and cook for 1 minute. Add the wine, orange juice, vinegar and honey, and bring to a boil. Lower the heat and simmer gently until reduced to about 1 cup (250 ml), about 30 minutes.
Meanwhile, in another saucepan, bring the veal stock to a boil, then let it reduce to about 1 cup (250 ml) over low heat, about 30 minutes.
Strain the wine mixture through a fine sieve set over the pan of reduced veal stock, pressing down on the vegetables to extract maximum flavor; discard the solids. Stir the sauce, then continue to cook over low heat until slightly thick, about 15 minutes. Add the butter, whisking constantly. Season with salt and pepper. Keep warm.
Preheat the oven to 400 degrees F (200 degrees C).
For the duck breasts:
Score the duck on the skin side. Remove the excess fat around the breast, and remove the tip, if desired. Sprinkle with salt and pepper. Place the duck breast, skin-side down, in a room-temperature skillet with no oil. Set the skillet over medium-high heat and cook for 5 minutes. Transfer the skillet to the oven and cook until medium-rare, 8 to 10 minutes. Let the duck breasts rest on a cutting board for about 5 minutes.
Slice the duck. Divide the Butternut Squash Gnocchi among plates. Top with the Roasted Fennel and duck. Add a spoonful of sauce and serve.
Butternut Squash Gnocchi:
Preheat the oven to 350 degrees F (180 degrees C). Line baking sheets with parchment paper and flour them to prevent the gnocchi from sticking.
Drizzle 2 tablespoons olive oil over each squash half and season with salt and pepper. Place on a baking sheet, cut-sides down, and bake for 1 hour. Let cool.
Scoop the flesh of the squash into the bowl of a food processor. Add the eggs, flour, 1 teaspoon salt and some pepper. Process just until the dough is soft (depending on the size of the squash, you might need more flour). Do not over mix.
Transfer the dough to a floured surface. Roll portions of dough into long ropes that are 2 centimeters (about 3/4-inch) in diameter. Cut ropes crosswise into pieces that are 2 centimeters (about 3/4-inch) long. Transfer the prepared baking sheet.
Bring a large pot of salted water to a boil. Cook the gnocchi until they float to the surface, about 2 minutes. Transfer the gnocchi with a slotted spoon or wire skimmer to a bowl of icy cold water to stop the cooking process. Drain.
Heat 2 tablespoons olive oil in a skillet over medium-high heat. Saute the gnocchi until golden. Add the veal stock and butter, and season with salt and pepper. Continue to cook until the gnocchi are golden brown, about 5 minutes. Stir in the chives and cheese.
Preheat the oven to 400 degrees F (200 degrees C). Heat the oil in a skillet over medium-high heat. Add the fennel and season with salt and pepper. Cook, turning to sear all sides, until caramelized, about 5 minutes. Transfer the skillet to the oven and roast for 30 minutes.