Heat butter and olive oil in a large skillet over medium heat. Add sliced onions and cook slowly for about 20 minutes until soft, golden, and sweet. Stir often so the onions do not burn.

Mix the minced garlic into the cooked onions and stir gently for one minute until fragrant. The garlic adds warmth and rich flavor without overpowering the sweet caramelized onions.

Push the onions to one side of the skillet and add the ground beef. Break the meat apart with a wooden spoon and cook until browned completely with no pink remaining.

Sprinkle onion powder, dried thyme, salt, and black pepper over the beef mixture. Add Worcestershire sauce and stir everything together well so the flavors blend nicely throughout the skillet.

Sprinkle flour over the beef and onions, then stir carefully until coated evenly. Slowly pour in beef broth while mixing constantly. Let the sauce simmer until slightly thick and glossy.

Reduce the heat to low and sprinkle shredded Gruyère cheese over the beef mixture. Cover the skillet for two minutes so the cheese melts smoothly into the savory filling.

While the cheese melts, lightly toast the hamburger buns in another pan or oven. Toasted buns hold the filling better and add a delicious crunch to every bite.

Spoon the hot beef mixture onto the toasted buns and garnish with fresh parsley if desired. Serve immediately while warm, cheesy, and full of rich French onion flavor.