In a medium saucepan, cook the bacon over medium-low heat until crisp, 7 to 10 minutes. Drain off all but about 3 tablespoons of the bacon fat and reserve the rest for later. Leave the bacon in the pan.
Add the onions and garlic and sauté until the onion is tender, about 5 minutes.
Stir in the caraway seeds and cook for 1 more minute.
Add in the sauerkraut, beer, bay leaf and 1 tablespoon of Lost Capital Mustard and bring to a simmer over medium heat. Reduce the heat to low and cook for 1 hour.
With 20 minutes remaining, heat the oven to 350 F.
Heat a cast-iron pan to medium-high heat and cook the bratwurst, turning occasionally, until the internal temperature reaches 150 F on an instant-read thermometer.
With a small, sharp knife, slice the sausages lengthwise about two-thirds of the way down so you can fold them open.
Wipe out the cast-iron pan, pour in about 2 tablespoons of reserved bacon fat, and bring the pan to medium-high heat. Sear the sausages in the bacon fat, cut-side down, for about 5 minutes until they are golden brown and crispy.
Transfer the bratwurst to a sheet pan, cut-side up, and sprinkle each one with about 2 tablespoons of Swiss cheese. Put the buns on the sheet pan cut-side up, and then slide the pan in the oven until the cheese melts, about 3 minutes.
Remove the sauerkraut mixture from the heat and stir in the chives.
Place the bratwursts inside the toasted buns, and top each with 2 to 3 tablespoons of the sauerkraut-and-bacon mixture and 1 tablespoon of Lost Capital Mustard. Serve hot.