Combine all crust mixture ingredients in a bowl and mix well with the butter as the binding ingredient.
Season the lamb with the salt and pepper. Sear the lamb on all sides with oil in a sauté pan and remove when golden brown. When cool, brush with Dijon mustard and cover with crust mixture. Place the mirepoix on a sheet pan and arrange the lamb on top. Roast in the oven at 375°F (190°C) until desired temperature.
To make the garlic mashed potatoes, cut the top from the garlic bulb, drizzle with olive oil, wrap in foil and bake for 1 hour in 350°F (175°C) or until tender. Remove and squeeze the garlic from the bulb and set aside. In another pot, combine cream, butter, salt, pepper, and roasted garlic paste and bring to a simmer. Place the potatoes in boiling salted water and cook for 25 minutes or until tender. Remove the potatoes and drain them and while hot, peel the potatoes and squeeze through a potato ricer into the garlic cream mixture. With a rubber spatula, stir until well incorporated while adjusting seasoning if needed.
To make the lamb rosemary au jus, heat the oil in a small saucepan over medium-high heat. Add the shallot, garlic, rosemary, salt, and pepper, then cook and stir. Add the stock and heat to a boil. Reduce the heat to medium-low and simmer until reduced. Remove from the heat and strain through a fine strainer.
To make the glazed carrots and broccoli, place the carrots in a saucepan with enough water to just cover them. Add the butter and granulated sugar and cook until the water evaporates, and the butter and sugar form a glaze. Blanch the broccoli in hot salted water and remove once tender then toss lightly with butter, salt, and pepper.
To serve, garnish a plate with 2 quenelles of the mashed potatoes. Arrange the broccoli and 3 baby carrots and the rack of lamb (3 bones) on the plate. Add the lamb au jus. Decorate the plate with rosemary and thyme bouquet.