Add the oil on a skillet over medium-high heat. Add the garlic and cook for 2 minutes. Add the beef and cook for 3-5 minutes. Add in the soy sauce and cook until there is no more rare/pink meat. Add the white pepper and set aside.
Fill a large bowl with warm water. Soak one piece of rice paper for 5-10 seconds until the paper becomes soft and easy to to mold.
Place butter lettuce, vegetables, a spoonful of beef, and mint leaves in a line on one side of the wrap, leaving an inch on each side of the wrap. Fold the bottom over the vegetables, fold in both sides of rice paper. Then roll tightly to top. Repeat until you have used all the ingredients.
Serve with Thai dipping sauce and sprinkle with lime juice.