Combine ginger, vinegar, fish sauce, lime juice, and sesame oil. Add pork chops, tossing to coat. Let rest and marinate for up to 8 hours.
Bring water to a boil in a medium saucepan. Add rice. Cover and reduce heat to low, cooking undisturbed for 15 minutes. Rice will be done when it is tender but firm. Remove from heat and stir in sesame oil and sesame seeds.
In a cast iron skillet over high heat, warm vegetable oil until smoking. Add shishitos and cook until blistered, about 2 minutes. Lower heat to medium, carefully toss peppers and fry for an additional 2-3 minutes. Remove from heat and season with salt and pepper to taste.
Over a grill on high heat, cook pork chops until crisped and browned, about 2 minutes per side.
Serve with pork chops and peppers over rice, and top with green onion and cilantro.