Place a large skillet over medium heat. Add the ground beef and cook, breaking it apart gently with a wooden spoon. Leave some small chunks for texture. Cook for 5–6 minutes, or until no pink remains.
Stir in the minced garlic and sesame oil. Cook for 1 minute, just until fragrant—be careful not to let the garlic brown.
Lower the heat slightly and pour in the ketchup, hoisin sauce, water, soy sauce, rice wine vinegar, and sriracha. Stir everything together until the beef is fully coated.
Let the mixture simmer for 5–6 minutes, stirring occasionally, until the sauce thickens and clings to the beef. It should look glossy and slightly sticky—if it’s too watery, let it simmer another 2 minutes.
While the beef mixture finishes, slice the brioche rolls and toast them lightly in a toaster or under a broiler for 1–2 minutes until golden.
Spoon the beef mixture generously over the bottom half of each roll. Sprinkle sliced green onions on top, then close with the other half of the roll. Serve warm.