Whisk together the soy sauce, cilantro, garlic, brown sugar, vegetable oil and lime juice in a bowl.
In a large baking dish, arrange the ribeye pork chops in an even layer. Pour the marinade over the pork chops, reserving about ¼ cup of the marinade in the refrigerator for later use.
Marinate the pork chops for 20 to 30 minutes.
Meanwhile, cook the pasta according to the package directions. Whisk together lime juice, garlic, peanut butter, hot water and soy sauce for the peanut sauce. Drain the pasta once cooked, and toss the pasta with the peanut noodle sauce in a large bowl. Add more soy sauce if desired.
Heat an indoor grill pan or outdoor grill to medium-high heat. Remove pork chops from the marinade, discarding the excess marinade. Place pork chops on the hot grill for 4 minutes on each side, flipping once until the internal temperature of the pork measures between 145°F. (medium rare) and 160°F. (medium) on a meat thermometer.
Transfer the grilled pork chops to a cutting board and let rest for 3 minutes before slicing against the grain.
Pour the reserved marinade over the sliced pork before serving and serve over the peanut noodles.