Heat the vegetable oil in a skillet or wok over medium-high heat.
Add the chopped onion and minced garlic to the skillet, cooking until softened, about 2 minutes.
Increase the heat to high and add the ground beef, breaking it apart with a spoon. Cook until browned, about 5-7 minutes. Drain excess fat if necessary.
Stir in the chopped mushrooms, red bell pepper, and shredded carrots. Cook for an additional 3-4 minutes, until the vegetables have softened.
In a mixing bowl, combine the soy sauce, hoisin sauce, rice vinegar, sesame oil, and minced ginger. Pour this sauce over the beef mixture and stir well to combine. Let it cook for 1-2 minutes, allowing the flavors to meld together.
Remove from heat. Stir in the sliced green onions and season with salt and pepper to taste.
To serve, spoon the beef mixture into the center of a lettuce leaf, fold it up, and enjoy!