Heat the vegetable oil in a large heavy-based pan over a high heat. Lay the pork medallions in the pan and cook, without turning, for 2-3 minutes until golden-brown. (You may need to brown the pork in batches to avoid overcrowding the pan.)
Add the butter to the pan then turn the medallions over and cook for 1-2 minutes until browned on the other side. Transfer the pork to a warm plate and set aside.
Pour the Bourbon into the pan to deglaze, using a wooden spoon to scrape up any flavoursome brown bits stuck to the bottom of pan.
Tip in the onion and garlic, reduce the heat to medium and sweat for 5 minutes, without colouring, until softened and translucent.
Turn the heat back up to high, pour in the chicken stock and the soaked pearl barley and bring to the boil. Reduce the heat and simmer vigorously for 15-20 minutes or until the volume of liquid has reduced by half.
Pour in the cream and whisk in the mustard. Season, to taste, with salt and freshly ground black pepper then stir in the additional tablespoon of Bourbon and the chopped tarragon.
Tip the pork medallions into the sauce, along with any juices on the plate, and simmer for 2-3 minutes until heated through.