Step 1Heat the oven to 350 degrees. Cook the garlic sausage in olive oil in the bottom of a Dutch oven over medium heat on the stove top until the sausage has browned, about 7 minutes. Add the carrot and cook until it begins to soften, about 5 minutes. Add the onion and cook, stirring constantly to scrape up any browned sausage bits sticking to the bottom of the pan, until it begins to soften, about 2 to 3 minutes. Add the garlic and cook until fragrant, about 3 minutes.
Step 2Add the dried beans, water and bay leaf. Bring to a simmer, stirring occasionally. Cover tightly and bake in the oven for 1 hour. Add the salt, stir, and continue cooking, covered, until the beans are tender, 45 minutes to 1 hour. The beans should be fairly dry, but if necessary, add more water, one-quarter cup at a time. Remove the bay leaf and discard. Season to taste with more salt if necessary, and freshly ground black pepper. (The dish can be prepared up to this point a day ahead and refrigerated, tightly covered.)
Step 3When almost ready to serve, chop the dandelion greens in 1-inch sections down to where you're getting almost all stem. You should have 3 to 4 cups.
Step 4While the duck breasts are cooking (below), reheat the beans, adding a little more water if necessary to create a slightly flowing, risotto-like texture, and add the dandelion greens. Cook, covered, until the greens soften, about 5 minutes. Season to taste with more salt and pepper, if necessary, and the red wine vinegar to taste.
Step 1Grind together the salt, cloves and peppercorns to a fine powder. Use a sharp knife to cut a shallow cross-hatching on the skin side of the duck breasts, through the skin but not to the meat.
Step 2Season the breasts on both sides with the spice mixture, concentrating on the skin side (you'll use most, if not all, of the spice) and place on a plate. Cover tightly with plastic wrap and refrigerate. (This recipe may be prepared to this point up to a day in advance; bring the duck to room temperature before continuing.)
Step 3Heat the oil in a large, heavy-bottom skillet over medium-high heat until it is hot but not smoking. Pat dry the skin side of the duck breasts with a paper towel and place the breasts skin-side down in the hot pan. Sear until the skin side is a deep golden brown, 4 to 5 minutes. Depending on the size of the skillet, the breasts will probably need to be cooked in batches. Press down on the breasts from time to time with a spatula to press out any rendered fat. Reduce the heat to medium and turn the breasts over. Cook on the second side until they are medium-rare in the center, 3 to 5 minutes more.
Step 4Remove the duck breasts to a carving board and let rest for 5 minutes before slicing on a bias into thick slices.
Step 5Spoon a generous three-quarters to 1 cup of white beans onto the center of a plate and arrange a sliced duck breast on top. Repeat, using all of the duck breast; you will have some white beans left over for another meal.