In a large skillet, heat the vegetable oil over medium heat. Add the minced garlic and sauté for about 30 seconds until fragrant.
Add the ground beef to the skillet, breaking it apart with a spatula. Cook until browned and fully cooked, about 5-7 minutes.
Stir in the soy sauce, fish sauce, lime juice, and season with salt and pepper. Cook for an additional 2 minutes, allowing the flavors to meld.
Remove the skillet from heat and stir in the fresh basil leaves until wilted.
To assemble the rolls, take a lettuce leaf and spoon a portion of the beef mixture into the center. Fold the sides of the leaf over the filling and roll it up tightly.
Repeat with the remaining lettuce leaves and beef mixture. Serve immediately or chill for 10 minutes before serving for a refreshing touch.