Peel the carrots, parsnips, and celery root, then cut them into small pieces. In a large pot, heat a bit of oil over medium heat and add the chopped vegetables. Sauté for about 2-3 minutes, stirring occasionally, until they begin to soften and develop flavor.
In the meantime, portion the hen. Wash the hen under lukewarm water. Use a sharp knife to portion it into smaller pieces, leaving the skin and bones intact. Place them into the pot with the sautéed vegetables.
Remaining vegetable use the whole. Add the whole. Add the Brussels sprouts, kohlrabi, the onion cut in half with the skin on (for the color), garlic cloves, ginger, spices and fresh parsley, and a sprinkle of nutmeg. Then, add enough cold water to cover the hen pieces completely. Bring the mixture to a boil.
Like any consommé, húsleves is best cooked when gently simmered and then carefully strained to remove any impurities. Reduce to low heat and cover the pot. Let the soup simmer for 1.5 to 2 hours, or until the meat and the vegetables are tender and fully cooked.
Carefully remove the chicken and vegetables from the soup using a large fine sieve, transferring the broth into a clean pot. Taste and season with pinch of salt if needed. Allow the meat and veggies to cool slightly. Discard the chicken skin and bones, chop the meat, and set it aside. Discard the whole onion and any pieces of bell pepper and spices. then chop the remaining vegetables and set them aside.