Melt butter in a large pot over medium-high heat. Cook beef in hot butter until browned on all sides. Pour in 4 cups water and bring to a boil. Add onion, salt, and pepper. Reduce heat to low and simmer for 1 hour.

Add potatoes, carrots, and celery; simmer for 1 1/2 more hours.

Whisk together remaining 1/2 cup water and flour in a small bowl to form a thin paste; stir into soup and simmer until thickened, about 15 minutes.