Make the onions: Heat the butter in a medium skillet over medium heat. When melted, add the onion and cook until softened and tender, about 20 minutes. When the onion is done, add a splash of water and stir in the mustard. Place the sauerkraut in a small saucepan and keep warm over low heat.
Make the sauce: Stir the sour cream, ketchup, and relish together in a a small bowl; season with salt and pepper.
Make the burgers: In a large bowl, combine the ground meats, celery seeds, marjoram, ginger, nutmeg, cardamom, parsley, and vinegar; season with salt and eppper and mix thoroughly. Score the mixture into 4 equal portions and form them into patties slightly thinner at the center than at the edges for even cooking and to ensure a flat surface (burgers plump as they cook). Heat the EVOO, 1 turn of the pan, in a large nonstick skillet over medium-high heat. Cook the burgers, flipping once, 10 to 12 minutes, or until the juices run clear. Top the burgers with the Swiss cheese for the last minute or two of cooking, tenting the skillet with aluminum foil, if you like, to help melt the cheese.
Pile the onions on the roll bottoms and top with the burgers. Top with sauerkraut and sour cream sauce. Set the roll tops in place.