Preheat oven to 375 degrees F (190 degrees C).
Mince the Shallot (1) and set aside.
Juice the Orange (1) into a small bowl; remove any seeds. Discard any seeds; hold.
Finely chop only HALF of the Dried Cherry (2 tablespoon); set aside.
Add the Chicken Base (1 package) and Water (1/4 cup) in a small bowl and stir until dissolved; hold.
Cut off the lower 1 inch from the Broccolini (8 ounce) stems; hold.
Pat the Lamb (1 rack) dry with paper towels. Season on both sides with Salt (1 teaspoon) and Ground Black Pepper (1/2 teaspoon).
Heat Olive Oil (1 tablespoon) in a large sauté pan over medium-high heat. When hot, sear lamb (fat side down) for 3 minutes.
Turn the lamb over and sear the other side for 3 minutes more. Transfer to a plate and hold for next step.
In the same large sauté pan you used for the lamb, add the broccolini. Season with Salt (1/4 teaspoon) and Ground Black Pepper (1/4 teaspoon). Toss in the pan drippings and push the broccolini to one side of the pan, leaving room for the lamb.
Return the lamb to the pan and place in the oven to roast for 8 to 10 minutes. Remove from oven and let rest.
Melt Unsalted Butter (1 tablespoon) in a small sauté pan over medium heat. Add the shallots and sauté for 2 minutes.
Stir in orange juice, cherries, Red Wine Vinegar (2 tablespoon), Port Cooking Wine (1/4 cup), and Granulated Sugar (4 package) and simmer for 4 minutes.
Add the Star Anise (1) chicken broth and stir. Simmer for 5 to 6 minutes. Add the remaining Unsalted Butter (1 tablespoon) and stir to combine well. Remove from heat and discard the star anise.
After the lamb has rested for at least 5 minutes, slice the lamb into 4 equal double chops by guiding your knife alongside the bone and thru the "chine" bone. Set aside for plating.
Divide the broccolini equally between two plates. Arrange the lamb chops on top of the broccolini. Spoon the gastrique over the lamb. Serve and enjoy!