To make the winter salsa, finely dice the carrots, fennel bulb, jerusalem artichokes and celery. Toss with the lemon juice, lemon zest and hazelnut oil in a bowl. Add smoked salt (or regular salt) to taste and set aside. (You'll add the green herbs later.)
To make the acorn dumpling dough, put the milk, duck fat and salt to a simmer in a small pot. Whisk in the acorn and regular flour, turn the heat to low and stir until the dough starts to come off the sides of the pot. Turn off the heat and let the dough cool for about 10 minutes. Stir in the egg and grated nutmeg, then move the dough to a bowl. Cover and let it stand for at least 20 minutes and up to overnight.
Take the duck breasts out of the fridge and salt them well. Let them sit on the counter for 30 minutes or so while the dumpling dough rests. While this is happening, Bring a large pot of water to a boil, then salt it so it tastes a little salty -- not as salty as pasta water. Once it boils, reduce the heat to a bare simmer for now.
Pat the duck breasts dry with a paper towel. If the duck is fatty, put the 2 teaspoons of duck fat in a large saute pan and turn the heat to medium-high. When it melts, add the duck breasts skin side down. If the duck is not fatty, do the same thing, but let the pan get hot first. Cook the skin side of the duck breasts on medium heat (it should sound like sizzling bacon) until the skin is brown and crispy, about 6 minutes. Turn the breasts over and use the finger test for doneness to determine when they're ready; I like my duck medium-rare. Take them off the heat and let them rest on the cutting board.
While the duck breasts are cooking, turn the heat up on the water to a solid simmer, but still not a boil. Shape the acorn dough into dumplings the size of a walnut with wet hands. Gently drop them into the simmering water and let them cook for a minute or two. Use a spoon or something to nudge them off the bottom of the pot, so they can float when they are cooked through. Once the dumplings float, let them cook another minute and them move them to a shallow pan. Gently coat them with a little hazelnut oil. Repeat with the rest of the dough.
Once the duck breasts are resting, add the green herbs to the winter salsa. Slice the duck breasts and serve skin side up, with a little drizzle of the hazelnut oil, with the dumplings and salsa on the plate.