PREHEAT THE OVEN to 400°F. Pat the roast dry and sprinkle all over with 1 teaspoon of the paprika, 1/2 teaspoon of the granulated garlic, . teaspoon of the granulated onion, and some salt and pepper. Heat half of the olive oil in a large Dutch oven over medium-high heat. Add the pork and brown on all sides, about 6 minutes. Transfer to a plate.
Add the remaining olive oil to the pot. Add the sliced onion and cook, stirring, until wilted and light golden, about 5 minutes. Add the apples and sauerkraut and cook until the sauerkraut begins to brown on the edges, about 4 minutes. Season with the remaining 1 teaspoon paprika, 1/2 teaspoon granulated garlic, and 1/2 teaspoon granulated onion and some salt and pepper (easy on the salt, sauerkraut is salty on its own). Add the thyme, garlic, and bay leaves. Increase the heat to high and add the hard cider. Bring to a boil and cook until reduced by half, about 2 minutes. Add the brown sugar and chicken broth and return to a simmer. Put the pork, bone side down, on top of the sauerkraut and cover the pot.
Transfer to the oven and bake until the pork reaches 145°F on an instant-read thermometer, about 45 minutes. Remove the pork to a cutting board and let rest for 10 minutes.
Meanwhile, bring the sauerkraut and cooking juices to a boil over medium-high heat. Whisk in the butter and boil until the juices thicken slightly, about 2 minutes. Discard the bay leaves. Carve the pork roast and serve on a bed of the sauerkraut and apples.