In a small bowl mix together the mustard, 2 tsp salt, and 1 tsp black pepper until well combined.
Rub the mustard mixture all over the pork tenderloins.
Heat 1 TBSP of the oil in a dutch oven over medium heat until hot.
Add one of the pork tenderloins to the dutch oven and sear until browned on all sides, 1 to 2 minutes per side.
Transfer the pork tenderloin to a plate and set aside then add the remaining 1 TBSP of oil to the dutch oven and sear the other pork tenderloin the same way, transferring it to the plate with the other pork tenderloin when browned.
Keep the dutch oven over medium-high heat and add the sauerkraut, onion, and apple then cook, stirring occasionally, for about 3 minutes.
Nestle the pork tenderloins back into the dutch oven on top of the sauerkraut then put the lid on the dutch oven and place in the oven until pork is cooked through, about 20 minutes.
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