Peel and dice the onions. Rinse the soup vegetables and cut into cubes. Rinse the tomatoes, remove the stalks and cut into cubes. Pour the soup vegetables, tomatoes and 2 liters (approximately 8.5 cups) of water into a pot. Season with caraway seeds and paprika. Simmer over low heat for about 90 minutes. Rinse the peppers, quarter, remove the seeds and place on a baking sheet, cut side down.
Grill the peppers in the oven for about 7 minutes, until the skin starts to blister. Remove from the oven and cover with a damp cloth for 10 minutes. Peel the peppers and cut into pieces. Peel, rinse and dice the potatoes. Pour the potatoes into a pot.
Pour 3/4 liter (approximately 3 cups) of the broth through a sieve over the potatoes. Cook for about 20 minutes. Halfway through cooking, add the peppers. Rinse the chives, drain and chop. Peel the horseradish, rinse and grate. Add the chives and horseradish to the soup. Season with salt and pepper. Serve immediately.