Preheat the oven to 165 °C (330 °F).
In a bowl, add the beets, potatoes and a third of the olive oil. Season with salt and pepper, and mix.
Place the duck roast on a baking sheet lined with parchment paper. Brush the roast with the rest of the olive oil. Arrange the vegetables around the duck roast.
Roast in the oven for 2 to 2.5 hours, until a cooking thermometer inserted in the roast reaches a temperature between 65 °C and 68 °C (150 °F and 154 °F).
Remove the roast from the oven and place on a cutting board. Cover loosely with a sheet of aluminum foil. Let stand for 15 to 20 minutes before slicing.
In the meantime, heat the duck fat in a saucepan over medium heat. Sauté the shallots for 1 to 2 minutes.
Add the port to the pan and flambé. Cook until the liquid has almost completely evaporated.
Add the duck stock, balsamic vinegar and herb mixture. Bring to a boil, then simmer for 1 to 2 minutes over medium-low heat.
Add the chocolate and the cream to the pan. Stir gently until the chocolate melts.
In a bowl, dissolve the cornstarch in a little cold water. Add the diluted cornstarch to the pan. Stir, then bring to a boil. Simmer until thickened. Season with salt and pepper, and stir.
Slice the duck roast into ½-inch (1 cm) slices.
Divide the sliced duck meat among the plates and drizzle with the sauce.
