Making the potatoes: Set a large saucepan filled with cold water over high heat. Add enough salt to the water to make it taste like the ocean. Add the potatoes. Bring to a boil, then reduce the heat to medium-high. Simmer until you can slide a knife right through one of the potato pieces without any force, 10 to 15 minutes.
Ricing the potatoes: Pour the potatoes into a large colander and shake to make sure all the water is out. Let the colander sit in the sink for 3 to 4 minutes to steam the potatoes dry. If you own a potato ricer or food mill, push the potatoes through. Or, you can push the potatoes through a fine-mesh sieve with the back of a ramekin or ladle.
Finishing the potatoes: Put the potatoes back into the pot you cooked them in. Stir the softened butter into the potatoes. Add the cream, egg, and olive oil and stir with a rubber spatula until the potato puree is silky smooth.
Browning the meat: Set a large skillet over medium-high heat. Pour in the oil, and then add the ground lamb. Cook, stirring occasionally, until the lamb is thoroughly browned. Remove from the pan and set aside.
Sauteing the vegetables: Add the onions to the pan in which you cooked the lamb, along with the garlic. Cook, stirring frequently, until the onions are soft and translucent, about 5 minutes. Add the pepper, mushrooms, and carrots and cook until the carrots are softened, about 5 minutes. Add the lavender and rosemary and cook until they release their fragrance, about 1 minute. Add the meat back to the vegetable mixture and remove from heat.
Making the sauce: Pour in the red wine. Cook, stirring occasionally, until the wine has reduced by half its volume. Add the chicken stock and bring it to a boil. Combine the cornstarch and water and stir until you have a thick slurry. After the chicken stock has simmered for a moment, pour in the slurry and stir the mixture thoroughly. This will thicken the liquid into gravy.
Finishing the shepherd's pie: Turn on the oven to broil. Transfer the meat and vegetable mixture to a large pie pan. Top with the potato puree. Cook under the broiler until the potatoes have turned a dark golden-brown, about 10 minutes.