For the caraway crust: Preheat the oven to 425 degrees F.
Place each bulb of garlic on a piece of tin foil, drizzle oil over and season with salt. Wrap the tin foil tightly around the bulbs, place in the oven and roast until golden and soft, about 45 minutes. Remove from the oven. Squeeze the roasted garlic into a small bowl; add the caraway seeds, brown sugar and mustard and mix to incorporate. Set aside until ready to crust the pork loin.
For the caraway crusted pork loin: Preheat the oven to 410 degrees F.
Score the pork fat in a crosshatch pattern, 1-inch apart. Spread and rub the caraway crust all over the pork loin and sprinkle with salt and pepper. Place the pork rack on the bottom of a large roasting dish, place the pork loin on the pork rack and place in the oven. After 10 minutes, reduce the heat to 350 degrees F. Once the crust has browned, after about 30 minutes, place a piece of tin foil over the top to prevent the crust from burning. Roast until the pork is cooked and reaches an internal temperature of 155 degrees F, about 1 1/2 hours. Remove from the oven and rest 15 minutes before slicing.
For the stewed cabbage: Heat the oil in a large, wide-mouthed saute pan over medium heat. Add the garlic, ground caraway and onions and cook until the onions are tender and translucent. Add the cabbage and stir to incorporate the ingredients. Add the chicken stock, white wine and apple cider vinegar and stir. Add the sugar, sprigs of thyme and cinnamon stick and season with salt and pepper. Cook until the cabbage becomes tender and liquid has mostly reduced, about 20 minutes.
For the sauteed apples: Heat the butter and oil in a saute pan over medium to high heat. Add the apples and saute until slightly caramelized and tender. Add the sugar and apple cider vinegar, season with pepper, stir and remove from the heat.
For the caraway mustard sauce: Place the yogurt, mustard, honey, thyme and caraway in a bowl and mix together. Reserve.
For the yellow bean salad with warm vinaigrette: Heat the olive oil in a medium saute pan over medium heat. Add the shallots and saute until tender and translucent. Add the olives and lemon juice to the pan. Allow the liquid to reduce slightly, add the blanched yellow beans, toss and remove from the heat.
Slice the pork loin and serve with the stewed cabbage, sauteed apples, caraway mustard sauce and yellow bean salad with warm vinaigrette.