Prep the ingredients per the instructions above.
Prep Salad: Arrange ingredients in a bowl.
Make the vinaigrette: In a bowl whisk together all the ingredients for the dressing until fully combined. Set aside.
For the mashed potatoes: Peel and cut potatoes into bite-sized chunks so they all cook evenly.
Place the potatoes in a pot with cold water over high heat. Once boiling, turn the heat down to a simmer. Check the potatoes by inserting a fork into them; once the fork slides in and out with ease, take off the heat and strain out all of the water.
For the potatoes: In a saucepan on medium low heat, heat the butter and milk until the butter is just melted. (You want to avoid boiling the milk.) Set aside until ready to use.
Make the carrots: Place the carrots in a small pot and cover them with water. Bring the carrots to a simmer and cook for about 6 - 10 minutes or until the carrots are tender. Drain off any excess water. Add the butter, brown sugar, and salt to the pan. Stir to coat the carrots. Cook for an additional 3 - 5 minutes, stirring occasionally until a sauce has formed. Then remove from the heat.
Mash the potatoes with a masher or potato ricer. Then pour half of the melted butter/milk mixture over the potatoes, and fold it in until the potatoes have soaked up the liquid. Repeat with the remaining butter, and then again with the cream cheese, folding in each until just combined to avoid over-mixing. Season with salt and pepper to taste.
Preheat the oven to 350°F (176°C).
For the lamb: Season the lamb very well with salt. Heat the oil in a skillet over medium heat. Once the pan is hot, sear the lamb chops on both sides until they cook to your desired temperature (see below) using a thermometer.
Once the lamb is cooked to your liking place it on a cutting board to rest. Melt the butter in a saucepan over medium heat. Add the garlic and sauté for 2 to 3 minutes, until toasted. Remove from the heat. Stir in parsley.
Warm the roll in the oven for 2 to 3 minutes, if desired cut it in half and spread it with butter. Dress the salad.
Serve the lamb chops drizzled with garlic butter. Enjoy with mashed potatoes, salad, carrots, roll, and wine.