Melt the butter in a large pot over medium heat. Add the sliced onions and cook, stirring often, until they turn golden and soft, about 20 minutes.
Push the onions to one side of the pot. Add the ground beef and cook until it is browned, breaking it up with a spoon as it cooks.
Stir in the minced garlic and cook for one minute until fragrant.
Add the beef broth, dried thyme, diced potatoes, and Worcestershire sauce. Season with salt and black pepper.
Bring the mixture to a simmer, then reduce the heat and cook for 25 minutes until the potatoes are tender.
Taste and adjust salt and pepper if needed. Ladle into bowls and top with fresh thyme sprigs if using.