Preheat the oven to 180 °C (350 °F).
Grate the potatoes and the sweet potato. Place on a cloth and wring the cloth over the sink to extract as much water as possible.
In a bowl, combine the potatoes with the herbs, garlic, and 45 ml (3 tbsp) of the shallots. Season with salt and pepper.
In a large non-stick pan, melt a third of the butter over medium heat. Form four patties directly in the pan, using about 80 ml (⅓ cup) of the mixture for each patty. Lightly press down on the patties. Cook for 4 to 5 minutes, until the edges of the patties begin to brown.
Gently turn the patties over and continue cooking for 4 to 5 minutes.
Place the patties on a baking sheet lined with parchment paper. Repeat steps 4 and 5 two more times with the rest of the potato mixture, to make a total of 12 patties. Set aside.
Place the duck legs on another a baking sheet lined with parchment paper. Bake in the oven for 15 to 20 minutes.
Place the rösti in the oven and reheat for 5 minutes while the duck finishes cooking.
In a saucepan, bring the red wine and the rest of the shallots to a boil over medium heat. Simmer until the liquid has completely reduced.
Add the demi-glace, figs and blackcurrant jelly to the saucepan. Season with salt and pepper. Simmer for 5 to 7 minutes over medium-low heat.
Shred the meat of the duck legs.
Layer three rösti on each plate. Top each serving with the shredded duck and drizzle with the fig sauce.
