Heat the butter or oil in a large pot over medium heat. Sauté onion and garlic until soft and fragrant.
Add carrot, celery, and potato, cooking for 3–4 minutes until slightly softened.
Pour in the stock and bring to a boil. Reduce heat and simmer for 15–20 minutes, until vegetables are tender.
Add the sliced biltong and simmer for another 5 minutes.
Remove from heat and stir in the milk or cream. Blend partially or fully with a stick blender for a smoother texture if desired.
Add crumbled blue cheese and stir until melted and creamy.
Season with salt and black pepper to taste. Be careful with salt, as biltong and blue cheese are already salty.
Serve hot, garnished with chopped parsley or chives.