Prepare the sauce: In a small bowl, whisk together the rice vinegar, water, orange marmalade, sugar, soy sauce, Sriracha, and minced garlic. Set aside.
Cook the beef: Heat a large skillet over medium heat. Add the ground beef, garlic, and ginger, breaking the meat into crumbles as it cooks. Cook for 8-10 minutes or until no pink remains. Drain any excess fat.
Make the orange glaze: Stir the soy sauce, orange juice, sugar, and marmalade into the skillet with the beef. Sprinkle in the red pepper flakes for a hint of spice.
Thicken the sauce: In a small bowl, mix the cornstarch and cold water until smooth. Pour the mixture into the skillet, stirring continuously. Cook for 1-2 minutes until the sauce thickens and coats the beef.
Assemble the wraps: Lay lettuce leaves flat on a plate. Fill each leaf with a spoonful of cooked brown rice, a generous scoop of the beef mixture, shredded carrots, and green onions. Drizzle with any extra sauce and serve immediately.