Cook the Ground Beef : Heat a large skillet over medium-high heat. Add ground beef and cook, breaking it up with a spatula, until browned, about 5–7 minutes. Drain excess fat if necessary.
Sauté Aromatics : Add onion, garlic, and ginger to the skillet with the beef. Cook until onion is soft and translucent, about 2–3 minutes.
Add Sauce and Seasonings : Stir in hoisin sauce, soy sauce, rice vinegar, sesame oil, and red pepper flakes (if using). Cook for an additional 2–3 minutes until the mixture is heated through and slightly thickened. Taste and adjust seasoning with salt and pepper as needed.
Prepare Lettuce Cups : Wash and dry lettuce leaves carefully to avoid tearing. Arrange leaves on a serving platter.
Assemble the Wraps : Spoon a portion of the beef mixture into each lettuce leaf. Top with shredded carrots, green onions, cilantro, and chopped nuts if desired. Serve with lime wedges for added brightness.