Move an oven rack to the middle position and heat the oven to 350°F.
Pat the pork tenderloin dry with a clean paper towel and season it evenly on all sides with 1/2 teaspoon kosher salt and 1/4 teaspoon freshly ground black pepper.
Heat 1 Tablespoon of the canola oil over medium-high heat in a saute pan or a large oven-safe skillet. Add the pork tenderloin and brown it evenly on all sides. Reduce the heat to medium and transfer the pork to a large plate.
Add the remaining 1 Tablespoon of canola oil, the sliced onion, and 1/4 teaspoon caraway seeds. Cook the onion until it is softened. Add the drained saueurkraut, and continue to cook for another minute or two, scraping up any browned bits from the skillet.
Transfer the pork tenderloin and any accumulated juices from the plate back to the skillet, nestling the pork into the sauerkraut. Cover the skillet and transfer it to the oven. Roast for about 30 minutes, until the temperature at the center of the tenderloin reaches 145°F.
Transfer the tenderloin to a cutting board and cover loosely with foil. Let the pork rest for 5-10 minutes before slicing. Slice the tenderloin about 3/4" (about 2cm) thick, and serve with some of the sauerkraut/onion mixture. Serve with noodles, roasted potatoes, spaetzle, or dinner rolls.