1. In a large skillet, over medium-high heat, cook the bacon until crisp, 6 to 8 minutes. Transfer to a paper towel-lined plate; let cool.
2. Heat grill to medium-high. Form the beef into four ¾-inch-thick patties. Use your fingers to make a shallow well in the top of each patty. (This will prevent overplumping during cooking.) Season with a total of ½ teaspoon each salt and pepper.
3. Oil the grill and cook the patties with the wells facing up for 4 to 5 minutes. Flip and cook until an instant-read thermometer inserted in the center registers 155° F for medium, 4 to 5 minutes more. Cut the bread in half crosswise and, dividing evenly, spread with the mustard. Form sandwiches with the bread, burgers, bacon, and sauerkraut.
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