Toss the pork pieces with the thyme, 1/4 teaspoon salt and 1/4 teaspoon pepper. Heat 1/2 of the oil in a medium Dutch oven over medium-high heat. Add the pork pieces in a single layer and cook until lightly browned, about 5 minutes. Transfer with a slotted spoon to a bowl.
Heat the remaining oil in the same pot and add the carrots, celery, onions and bell pepper and cook, stirring, until softened, 7 to 10 minutes. Stir in the paprika, tomato paste, caraway and garlic until fragrant and the tomato paste has darkened slightly, 1 to 2 minutes. Stir in the broth and 1 1/2 cups water and bring to a simmer. Cook until the vegetables are tender and the broth has thickened, about 45 minutes.
Meanwhile, cook the noodles according to package directions and keep warm.
Add the pork back to the stew and cook, stirring, until the pork is cooked through and hot. Stir in the vinegar and season with salt and pepper. Toss with the hot egg noodles and garnish with chives.