Cut the pork shoulder into 1-inch cubes, ensuring any large pieces of surface fat are trimmed away to keep it clean.
In a large glass bowl, whisk together the gochujang, tamari, honey, toasted sesame oil, grated ginger, and minced garlic until smooth.
Add the pork cubes to the bowl and toss thoroughly to coat, then let marinate in the refrigerator for at least 30 minutes to develop flavor.
Thread the marinated pork onto wooden or metal skewers, leaving a small space between each piece for even heat distribution.
Preheat a grill or grill pan to medium-high heat and cook the skewers for 3 to 4 minutes per side until beautifully charred and cooked through.
While the pork cooks, thinly slice the cucumber and toss it in a small bowl with the rice vinegar and sea salt for a quick pickle.
Transfer the skewers to a serving plate, garnish with sesame seeds, and serve immediately alongside the chilled cucumber salad.