For the chorizo, combine the duck, vinegar, salt and all of the spices and mix together in a bowl. Cover with plastic wrap and refrigerate for at least 2 hours, or overnight.
Using a meat grinder, grind everything through a medium die. Mix well by hand, cover and refrigerate for 1 hour.
Wash and sanitize all of the grinder parts and the machine, then pull out half of the duck mixture, grind through the medium die again and mix with the other half by hand. Divide the mixture in half.
In a medium saucepan, cook one half of the chorizo over low to medium heat to brown and render out some of the fat. Drain the fat and reserve. Set the cooked chorizo aside until ready to plate. Freeze the remaining half of the chorizo in an airtight bag for future use.
Prepare the duck breasts. Season the flesh side of the duck breasts with salt and pepper and place them, skin-side down, in a dry pan over low heat. Render the fat slowly until the skin starts to crisp (don’t add any additional oil or fat to the pan). Once the skin starts to crisp, use the rendered fat to baste the flesh side until the breasts are cooked medium-rare, to approximately 140°. Set aside to rest on a plate, then slice before serving.
Trim the top and bottom of each squash. Using a mandoline or a sharp knife, slice each squash lengthwise into 1/16-inch slices. Arrange the slices into several even stacks. Turn each squash stack on its side and slice in half again, lengthwise, to create long, pasta-like strands.
Heat the rendered fat from the chorizo then gently sauté the squash strands in the fat. Add the splash of warm stock, season with salt and pepper, then remove from the heat and divide into 4 bowls. Top each with some of the chorizo, then some of the sliced duck breast. Finally, garnish with mint marigold leaves and flowers.