How to Make It
Toss together scallions, lemongrass, salt, sugar, lime zest, and garlic in a bowl.
Trim and discard any skin (leave the fat) from pork shoulder and fatback; cut into 3- x 3/4-inch strips. Toss pork strips with scallion mixture; cover and chill at least 1 hour and up to 24 hours. Follow these instructions for grinding pork mixture through step 6.
Shape ground pork mixture into 12 (2-inch) patties. Heat oil in a large skillet over medium. Working in batches, cook patties until well browned and no longer pink in center, about 3 minutes per side. Remove from skillet; let rest 5 minutes.
Stack 2 lettuce leaves to form a cup; repeat with remaining leaves. Place 2 patties in each lettuce cup with matchstick carrots, mint, cilantro, and nuoc cham.
If asking your butcher to grind meat, substitute 1 1/4 pounds 70% lean ground pork for pork shoulder and fatback.