In a dry skillet over medium heat, place the onion halves cut side down and cook until they are dark brown and caramelized. This will add depth of flavor to the broth.
In a large pot, place the beef rump (Tafelspitz) and bone marrow (if using). Cover with cold water and bring to a boil. Skim off any foam that rises to the surface.
Add the caramelized onions, carrots, parsnips, leek, celery root, garlic, bay leaf, black peppercorns, and salt to the pot. Reduce the heat to low and let it simmer gently for about 2.5 to 3 hours, or until the beef is tender.
In a small bowl, combine the freshly grated horseradish, sour cream, lemon juice, salt, and pepper. Mix well and set aside.
In another small bowl, combine the grated apples, freshly grated horseradish, lemon juice, sugar, and salt. Mix well and set aside.
Remove the beef from the pot and let it rest for a few minutes before slicing.
Strain the broth and return it to the pot. Adjust the seasoning with salt and freshly ground black pepper as needed.
Enjoy your meal!