Preheat oven to 400 degrees F. Rub chicken breasts with 1 tbsp oil, salt and pepper. Bake in the preheated oven for 10 minutes. Flip chicken and cook until no longer pink in the middle and juices run clear, about 15 minutes more. Set aside.
In a large pot, warm 1 tbsp oil over medium heat. Add garlic, onion, sweet potatoes, celery root, potatoes, and carrots; season with salt and pepper. Cook, stirring occasionally, until vegetables soften and onion is translucent.
Add tomatoes, cabbage, and 6 cups water; cover and bring to a boil. Reduce heat to medium-low and simmer until vegetables are crisp-tender.
Chop cooked chicken breasts and add to the pot, cook until warmed throughout.