Cook the bacon in a 12-inch skillet over medium heat, turning occasionally with tongs, until crisp, 6 to 8 minutes. Remove the skillet from the heat. Transfer the bacon to a cutting board with a slotted spoon, let cool slightly, and chop into small pieces. Drain all but 2 Tbs. of the fat from the skillet.
In a large bowl, thoroughly mix the bacon, ground pork, caraway seeds,
and nutmeg with your hands. Form into four 1/2-inch-thick patties.
Return the skillet to medium heat. When the bacon fat is hot, add the
burgers and cook for 6 minutes. Flip the burgers, cover the skillet, and
continue to cook until an instant-read thermometer inserted into a
burger registers 160°F for well done, about 5 minutes more. Turn off the
heat, top each with a slice of the cheese, cover, and let sit until the
cheese has melted, about 1 minute.
Meanwhile, heat the sauerkraut in a small saucepan over medium heat until warm.
Spread mustard on each slice of rye toast. Serve the burgers between the toast, topped with the sauerkraut.