Adjust oven rack to middle position, place rimmed baking sheet on rack, and heat oven to 425 degrees. Toss potatoes with 2 tablespoons oil, 1/2 teaspoon salt, and 1.4 teaspoon pepper in bowl. In separate bowl, toss onions with 1 tablespoon of oil.
Place bratwurst on 1 side of hot sheet and spread potatoes, cut side down, on other side. Scatter onions around bratwurst on sheet. Roast until bratwurst registers 160 degrees and potatoes are tender, 25-30 minutes, flipping bratwurst halfway through roasting.
While bratwurst and vegetables are roasting, whisk 2 tablespoons mustard, vinegar, 1/2 teaspoon salt, 1/t teaspoon pepper and remaining 1/4 cup oil together in large bowl.
Remove sheet from oven. Add potatoes to bowl with dressing and toss to coat; cover to keep warm. Tent onions and bratwurst, still on sheet, with aluminum foil to keep warm. Place buns directly on rack and toast until lightly browned, about 5 minutes.
Remove buns from oven. Spread remaining 2 tablespoons mustard evenly into buns, then top with bratwurst and onions. Add kale and radishes to potatoes and toss gently to combine. Serve immediately with sandwiches.