In a medium skillet, bring 1 inch of water to a boil, reduce heat to simmer, pierce the casings of 4 pieces of bratwurst and set into a medium skillet. Simmer sausages 10 minutes, then remove to a cutting board, pour water out of pan and return pan to stovetop, adjusting heat to medium high heat. Slice sausages on an angle, 6 cuts per wurst. Add 1 tablespoon extra-virgin olive oil, 1 turn of the pan, and set slices into hot skillet. Brown 1 to 2 minutes on each side.
Place sauerkraut into a colander. Rinse and squeeze dry. Add to the browned bratwurst slices. Stir in sweet red pepper relish and warm through another 1 to 2 minutes. Transfer to a serving dish and place along side cocktail or quartered sliced dark bread. To serve, spoon sliced wurst and sauerkraut onto bread.