Rub the lamb with the fennel, salt and pepper. Heat a cast iron skillet over high heat with one turn of the pan of olive oil. Add the chops and brown them well on each side. Reduce the heat to medium; add the garlic, 4 tablespoons of butter and the thyme. Baste the meat with the butter as it cooks, about 10 minutes, turning once. Let rest for 5-10 minutes before serving.
Meanwhile, heat the remaining olive oil, a turn of the pan, in a second skillet over medium to medium-high heat. Add the remaining tablespoon butter and melt into the oil; when it foams, add the shallots. Stir for a minute or two, then add the peas and stock and simmer for 4-5 minutes. Season with salt and pepper and mash the peas with a potato masher. Add the herbs and mascarpone, and stir to combine. Adjust seasoning, to taste.
Top the chops with creamy peas (like a sauce) and serve with a pile of potato chips alongside.