Trim the outer layers and root end from the lemongrass, then finely mince the tender lower portion.
Finely mince the garlic and the shallot.
Combine the minced lemongrass, garlic, shallot, brown sugar, fish sauce, oil, soy sauce, lime juice, and black pepper in a large bowl.
Add the pork chops to the marinade and rub the mixture into all surfaces of the meat.
Cover and refrigerate for at least 4 hours or overnight.
Remove the pork from the fridge 30-45 minutes before grilling.
Preheat the grill to high (450-500°F).
Place the pork chops on the hot grates and sear undisturbed for 4-5 minutes.
Flip the chops and continue cooking, flipping every 45-60 seconds to prevent burning.
Cook until the internal temperature reaches 145°F (about 5-7 minutes more).
Let the chops rest on a cutting board for 5 minutes.
Slice and serve with jasmine rice.