Preheat oven to 475F.

Combine dry thyme, salt, and black pepper in a small bowl.

Sprinkle the seasoning mixture evenly over the rack of lamb.

Heat 1 tablespoon of olive oil in a large, heavy skillet over high heat.

Sear the lamb on both sides for 3 minutes per side until browned.

Pour off excess fat from the skillet, reserving any juices.

Transfer the seared lamb to a roasting pan.

Roast in the preheated oven, fat side up, for 13 to 15 minutes, or until the internal temperature reaches 130-135F for medium-rare.

Remove the rack of lamb from the oven and transfer it to a warm platter.

Let the lamb rest for 10 minutes.

While the lamb rests, return the skillet to the burner over medium heat.

Add chicken broth to the skillet and scrape up any browned bits from the bottom of the pan.

Reduce the broth to approximately 1 tablespoon.

Remove the pan from the heat and whisk in the remaining 3 tablespoons of olive oil and the chopped fresh mint.

Add balsamic vinegar and whisk to form the vinaigrette.

Cut the rack of lamb into individual chops.

Serve the chops atop a bed of mixed salad greens and drizzle with the fresh mint balsamic vinaigrette.