To prepare marinade, combine first 3 ingredients in a large zip-top plastic bag. Trim fat from steak. Cut steak diagonally across grain into thin slices. Add steak to bag; seal and marinate in refrigerator 2 hours. Remove steak from bag, and discard marinade.
To prepare dipping sauce, combine peanut butter and the next 4 ingredients (peanut butter through 1 teaspoon sugar) in a small bowl; stir with a whisk until blended. Set aside.
Place rice sticks in a medium saucepan; cover with hot water. Let stand 30 minutes. Bring to a boil, and cook 5 minutes. Drain; cut rice sticks into small pieces.
Heat oil in a large nonstick skillet over medium-high heat. Add beef; stir-fry 2 minutes. Add rice sticks; cook 1 minute. Stir in 1 tablespoon lime juice and chile paste. Remove from heat.
Place 1 lettuce leaf in the center of 1 crepe, and top with 1/4 cup beef mixture, about 1 tablespoon carrot, 3 cucumber slices, 3 mint leaves, and 3 cilantro sprigs. Fold in bottom of crepe, and roll up jelly-roll fashion starting at side. Repeat the procedure with remaining lettuce, crepes, beef mixture, carrot, cucumber, mint, and cilantro. Cut each roll crosswise into 3 slices; arrange, cut sides up, on a plate. Serve with dipping sauce.