Place all the mint julep sauce ingredients in the bowl of a blender or food processor. Process until the mint is finely chopped and everything is evenly mixed.
Pour the mixture into a small saucepan. Bring to a boil over medium heat. Reduce the heat and simmer until the sugar is dissolved and the alcohol in the bourbon is evaporated, no more than a minute.
Remove the pan from the heat and set aside. Sauce will thicken as it cools.
For the lamb chops:
Season both side of the chops with salt and pepper.
Heat 1-2 tablespoons of cooking oil in a large skillet over medium-high.
Once the oil is hot, place the chops in the skillet. You may have to do this in batches, don’t overcrowd the pan.
Sear the chops for one minute and thirty seconds on each side. Thicker chops may require a longer cook time, up to three minutes per side. Lamb chops should be cooked until they reach an internal temperature of 145 degrees F for medium rare, 160 degrees F for medium and 170 degrees F for well done.
To serve, place a few chops on a plate. Drizzle the mint sauce over the top. Sprinkle with additional chopped fresh mint on the side.