Heat the oil in a large skillet over medium-high heat until hot. Add the livers, making sure not to crowd the pan, and sear on both sides just until browned. Remove from the pan and set aside.
Add the shallots and garlic to the pan and caramelize. Season with salt and pepper to help release the juices. Add more oil as necessary.
Return the livers to the pan, then add the wine and port. Cover partially with lid and simmer until liquid has reduced by 2/3.
Remove from the heat and let cool for a few minutes, but not completely. Once partially cooled, place the mixture in a blender and puree until smooth. With the blender running, add the buttered followed by the cream. Continue to puree until smooth and creamy. Season with salt and pepper and transfer to a small bowl.
If you want the mousse especially silky, you can pass it through a fine mesh strainer at this point.
Season with balsamic vinegar and cider vinegar to taste.
Chill in the refrigerator until ready to eat.