In a large skillet, heat the vegetable oil over medium heat. Add the minced garlic and chopped onion, sautéing until the onion becomes translucent, about 3-4 minutes.
Add the ground beef to the skillet, breaking it apart with a spatula. Cook until browned, about 5-7 minutes.
Stir in the sliced red bell pepper, soy sauce, oyster sauce, sugar, and black pepper. Cook for an additional 3-4 minutes, allowing the flavors to meld.
Remove the skillet from heat and fold in the fresh Thai basil leaves, mixing until they are wilted.
To assemble the rolls, place a generous spoonful of the beef mixture onto a lettuce leaf. Fold the sides of the leaf over the filling and roll it up tightly.
Serve the rolls with lime wedges on the side for squeezing over the top.