Heat the vegetable oil in a large skillet over medium-high heat. Season the pork shoulder with salt and pepper, then sear it on all sides until browned, about 5-7 minutes total. Remove from heat.

In a slow cooker, combine soy sauce, brown sugar, rice vinegar, sesame oil, garlic, ginger, and red pepper flakes. Place the seared pork shoulder in the slow cooker, ensuring it is well coated with the sauce.

Cover and cook on low for 8 hours or high for 4 hours, until the pork is tender and easily shredded with a fork.

Once cooked, remove the pork from the slow cooker and shred it using two forks. Return the shredded pork to the slow cooker and mix it with the sauce.

Warm the tortillas in a dry skillet or microwave. Assemble the tacos by placing a generous amount of pulled pork on each tortilla, then top with shredded cabbage, sliced carrots, green onions, and cilantro.

Serve with lime wedges on the side for squeezing over the tacos.