Slice pork into 8 crosswise pieces. Press each pork tenderloin slice to 1- inch thickness. In a large heavy skillet, heat coconut oil over medium-high heat. Brown pork quickly, cooking for 1 minute on each side.
Remove from heat. Place cooked pork slices on serving plate, reserving drippings. Keep warm. Into the same skillet, add the next 4 ingredients (onions through black pepper). Cook over low heat about 2 minutes, stirring frequently.
Add balsamic vinegar; stir to blend. Return pork slices to skillet; season with salt and pepper. Spoon onion mixture over slices. Cover and simmer 3-4 minutes until pork is cooked through.