Preheat the oven to 425°F (218°C). Slice a crisscross pattern into the top layer of fat on the pork belly. Season the pork liberally with the salt and black pepper and place it skin side up in a 10-inch (25-cm) or larger cast iron skillet.
Bake the pork for 35 minutes. Reduce the heat to 325°F (163°C) and bake for 30 more minutes, until the top of the pork is crispy and golden. If needed, broil the pork for 4 to 5 minutes at the end of the cooking time to make sure the top is very crispy.
Remove the pork from the oven and let it rest for 15 minutes before slicing.
While the pork is resting, drain out all but 3 tablespoons (45 ml) of the fat in the skillet and place the skillet over medium-high heat. Working in batches, add the collard greens, garlic, and vinegar to the skillet. Cook the collards for 7 to 10 minutes, until they are very wilted. Turn off the heat and stir in the kimchi.
To serve, slice the pork belly and serve the slices with the collard greens.