Preheat the oven to 425 degrees F. Rub the pork all over with 2 teaspoons paprika and 1/2 teaspoon salt. Heat 1 tablespoon olive oil in a large Dutch oven or pot over medium-high heat. Add the pork and cook, turning until browned, 3 minutes. Remove to a rimmed baking sheet. Roast until a thermometer inserted into the center reaches 145 degrees F, about 18 minutes. Let rest 5 minutes.
Meanwhile, wipe the pot clean and heat the remaining 1 tablespoon olive oil over medium-high heat. Add the potatoes and cook, stirring occasionally, until lightly browned, 4 minutes. Stir in the cabbage, onion, the remaining 1 teaspoon paprika and 1/2 teaspoon salt. Cover and cook, stirring occasionally, until the cabbage wilts slightly, about 4 minutes.
Add the broth and brown sugar. Bring to a boil, then reduce the heat to medium low; cover and cook until the vegetables are tender, 8 to 10 minutes. Stir in the vinegar. Increase the heat to medium high; cook until the sauce is reduced, 4 minutes. Add the herbs. Slice the pork; serve with the vegetables. Top with the sour cream and more paprika.