Trim pork chops of fat and place in a small non-metallic container. Pour over the balsamic,oregano,brown sugar. Fill with water just to cover chops and mix around by hand. Brine 24 hours.
Slice romaine lengthwise in half keeping stem intact and set aside. Slice yellow squash about 1/2 inch thick. (Depending on the thickness you might end up with 3 separate pieces) and set aside.
Start your grill pan and give it a light coating of olive oil on a med-high heat. Place romaine flat side down and grill until carmalized ( about 3-5 minutes. Remove and set aside. Repeat with the squash and onion then set aside. Place cherry tomatoes in the same pan ( you might need a little oil) until somewhat lightly blackened and set aside.
Drain chops and blot dry. Clean grill pan and add a little oil and place chops in pan. Meanwhile in a food processor add the olive oil,sea salt,white wine vinegar, 6 reserved cherry tomatoes,fresh basil and pulse a few times. Set aside. Turn chops over and cook until desired doneness.
Chop up romaine and place on a platter. Add your other grilled veggies anyway you like followed by the pork chops and drizzle with the vinaigrette, Sprinkle feta cheese over salad.