Coat a wide pan with olive oil and bring to a medium-high heat. Sprinkle the lamb with salt and toss with the flour.
Add the lamb to the pan and brown well on all sides. Remove the lamb from the pan and reserve. Ditch the oil in the pan and add a splash new olive oil. Add the carrots, celery and leeks to the same pan. Season the mixture with salt and cook, stirring frequently until the vegetables are soft and very aromatic, 8 to 10 minutes. Add the garlic and cook 2 to 3 minutes more. Add the tomato paste and cook until the tomato paste starts to brown, 2 to 3 minutes.
Add the beer and cook until it reduces by half. Return the lamb to the pan. Add enough stock to just cover the surface of the lamb. Taste and season with salt if needed. Toss in the bay leaves and thyme bundle. Bring the stock to a boil and reduce to a simmer. Partially cover and simmer until the lamb is tender, about 1 hour. When the stock level reduces, replace with more to keep the meat submerged.
Place the potatoes in a medium saucepan and cover by 1 inch with tap water. Season the water with salt and bring the water to a boil. Boil the potatoes until they are fork tender, about 15 minutes. Drain the water from the potatoes and pass them while they are still hot through a food mill. In a small saucepan over medium-high heat, bring the cream to a boil. Beat the cold butter and hot cream into the pureed potatoes. Taste and season with salt if needed. The potatoes should be creamy and very flavorful.
Remove the lid from the lamb and add the peas. Simmer for 15 minutes more to allow the stock level to reduce. Taste and adjust the seasoning if needed. When done, the lamb mixture should be thick and stew-like. Remove the bay leaves and thyme bundle and discard.
Preheat the broiler.
Transfer the lamb to a wide, flat baking dish. Spread the mashed potatoes over the lamb mixture in an even layer. Place the baking dish under the preheated broiler. Broil until the potatoes are golden brown and crispy.