Sprinkle salt and pepper on the pork, then sear it on all sides in a pan over medium heat. Transfer it to an oven preheated to 350°F for 10 minutes or until the internal temperature reaches 135°F. Allow it to rest afterward.

In the same pan used for searing the pork, melt some butter and sauté the mushrooms until they are tender and most of the liquid evaporates. Deglaze the pan with Galliano and reduce until the liquid has evaporated. Add the tarragon, water, and demi-glace paste, and let it simmer for 5 minutes.

Then, pour in the heavy cream and bring to a boil for 1 minute, then simmer until it thickens. Incorporate any juices released from the resting pork.

Slice the pork, pour the sauce over it, and garnish with green onions. Serve with a side of vegetables and your favourite starch.