Slice the pork shoulder into very thin, bite-sized strips to mimic the texture of pork belly.
In a small bowl, whisk together the gochujang, tamari, sesame oil, minced garlic, and grated ginger until smooth.
Heat a large non-stick skillet over medium-high heat until very hot.
Season the pork strips with sea salt and black pepper, then add them to the skillet in a single layer.
Cook the pork until the fat has rendered and the edges are golden brown and crispy, approximately 5 to 7 minutes.
Pour the gochujang sauce mixture over the pork and toss continuously for 1 minute until the sauce becomes a sticky glaze.
Prepare the lettuce wraps by placing a portion of the crispy pork into each butter lettuce leaf.
Top the pork with julienned cucumber and shredded carrots for added texture.
Garnish with sliced green onions and serve immediately while the pork is hot and the lettuce is crisp.