Slice pork tenderloin medallions to desired thickness. You will need 8 large medallions. Pepper the tenderloin medallions with the black coarse ground pepper to taste then place pork tenderloins in a bag or container with a well-fitting lid. Add the teriyaki sauce and soy sauce and coat well. Marinate at least 2-3 hours for best results. Turn medallions in marinade at least once every hour.
Freeze any remaining medallions or increase recipe ingredients for more servings.
Peel onions and cut in half then slice onions and place aside. Place 3 tablespoons of butter and 1 tablespoon of olive oil in skillet. Add onions when the butter has melted. Coat onions well. After 10 minutes add one or two pinches of salt. Add 1 tsp of sugar after the onions have cooked about 20-30 minutes. Cook the onions for 30 minutes to 1 hour over medium heat until caramelized. In the beginning it won't be necessary to stir often but as the onions become more caramelized more stirring will be necessary as you don't want the onions to burn but to brown. Use a spatula to turn the onions and keep the onions from sticking and then when the onions are caramelized add the balsamic vinegar to deglaze the pan and coat the onions. To caramelize onions is a slow process but it is worth it.
Grill the pork tenderloin medallions . The thickness of the medallions will determine the length of time to grill. Grill pork until done but moist. The juices will run clear. Remove from grill to serving plate.
Top the grilled medallions with the caramelized onions. Serve.