Preheat oven to 425 degrees F.
In a 12 to 14-inch saute pan, heat oil over medium heat and add onions. Slowly cook the onions until they are soft and starting to turn light golden brown, about 10 to 12 minutes. Add balsamic vinegar and continue cooking for 20 minutes until very soft and tan, that is, caramelized. Meanwhile, place pancetta rounds on a cookie sheet lined with parchment and bake 8 to 10 minutes, until crispy and brown. Remove and place on a plate with paper towels to drain.
Place a 12 to 14-inch saute pan over high heat. Remove liver from milk, pat dry and dredge in seasoned flour. Pour remaining olive oil in pan and add liver, 3 pieces at a time, and quickly cook until dark golden brown, about 2 to 3 minutes. Turn and cook 1 minute on other side. Continue until all liver is done. When last liver is out, add caramelized onions to liver pan and splash with remaining vinegar. Replace liver in pan and cook until hot. Add parsley and put on a plate, placing pancetta over top.