01 - Preheat grill to medium-high heat (approximately 400°F).
02 - Heat vegetable oil in a skillet over medium heat. Add sliced onion and cook, stirring frequently, until softened and golden brown (about 8 minutes).
03 - Add drained sauerkraut and caraway seeds (if using) to the skillet. Stir and cook for an additional 3-4 minutes until heated through. Season with freshly ground black pepper.
04 - Place beef bratwursts on the preheated grill. Turn occasionally and grill for 12-15 minutes until evenly browned and fully cooked, reaching an internal temperature of 160°F.
05 - During the final 2 minutes of grilling, place buns cut-side down on the grill to lightly toast.
06 - Place a grilled bratwurst in each toasted bun. Top generously with the warm sauerkraut-onion mixture. Add mustard, ketchup, and pickles as desired. Serve immediately while hot.