Special equipment: Mandolin slicer
For the pork loin: Combine 2 quarts water, the salt, brown sugar, mustard powder, peppercorns and bay leaves in a large mixing bowl and stir until the salt, sugar and mustard powder have completely dissolved. Place a large resealable plastic bag into a bowl and then pour the brine into the bag. Submerge the pork in the brine, seal the bag and refrigerate for at least 4 hours and no longer than 6 hours.
Preheat the oven to 350 degrees F. Remove the pork from the brine, pat it dry and sprinkle it liberally with salt and pepper.
Heat the oil in a large ovenproof skillet over medium-high heat and brown the pork loin on all sides, about 8 minutes total. Turn off the heat and remove and discard any excess fat from the pan with a spoon. Roast the pork until a thermometer inserted into the center reads 140 degrees F, 35 to 45 minutes. Transfer to a board and let rest for 20 minutes.
Meanwhile, make the pan sauce. Pour out the fat from the skillet and reserve, and then heat the skillet over medium-high heat. Pour in the stock, scraping off any browned bits on the bottom using a whisk. Cook until the stock has reduced by half, 2 to 4 minutes, and then turn the heat down to low and whisk in the butter one piece at a time. Whisk in the mustard and season with salt and pepper. Transfer the sauce to a small saucepan and cover to keep warm.
For the brussels sprouts: Thinly slice the Brussels sprouts using a Japanese or French mandolin or a sharp knife. Wipe out the skillet used for the pan sauce and heat 3 tablespoons of the reserved pork fat over medium-high heat. Add the shallots and cook until slightly softened and lightly browned, 2 to 3 minutes, and then add the sprouts and sprinkle liberally with salt and pepper. Cook until the sprouts are tender yet crisp and starting to brown slightly, 3 to 5 minutes.
To serve, thinly slice the pork and place on a platter. Spoon the pan sauce on top and serve with the Brussels sprouts, German dumplings, and remaining pan sauce on the side.