Step 1 In a large bowl, mix together the ground pork, relish and a tablespoon of mustard. (The relish keeps the pork moist.) Do not overwork, but mix until ingredients are evenly combined. Divide the meat into 6 portions and form the burgers, matching the size to the buns.
Step 2 Heat a grill or grill pan over medium-high heat until hot. Place the burgers, then the bratwurst links, on the grill to start cooking.
Step 3While the burgers and links are grilling, start the bacon. In a skillet heated over medium-high heat until hot (use a cast iron skillet if cooking on the grill), render the bacon, stirring frequently, about 6 minutes. Add chopped onion to the skillet and cook until the onion is softened, stirring frequently, 6 to 8 minutes.
Step 4Stir in the sauerkraut with the bacon and onions, cooking down the mixture to marry the flavors. Continue to cook until the hamburgers and sausages are grilled on all sides, an additional 12 to 15 minutes. Remove the burgers, sausages and skillet from the heat, setting all aside to keep them warm. Cut the bratwurst into thin crosswise slices.
Step 5In a small bowl, whisk together the butter and remaining mustard; this makes about 2 cups spread, slightly more than is needed for the remainder of the recipe. The mustard butter will keep for 1 to 2 weeks, covered and refrigerated.
Step 6Spread or brush the mustard butter over the cut halves of each bun (about 2 tablespoons per half, depending on the size of the bun). Toast the buns on the cooler side of the grill or on the grill pan.
Step 7Assemble the burgers: Mound the sliced bratwurst on top of each burger (1 bratwurst per burger), then top with the sliced pickle, kraut, bacon and onion mixture. Divide the sliced Swiss cheese among the burgers, covering each mound of toppings with cheese. Place the burgers back on the grill or on the grill pan, closing the grill or covering the pan with a large roasting pan until the cheese is melted, 1 to 2 minutes. (You can also melt the cheese by placing the burgers on a baking sheet in a hot oven.)
Step 8Place the assembled burgers in the toasted buns and serve immediately.