How to Make It
In a large enameled cast-iron casserole, heat the olive oil until shimmering. Season the pork chops with salt and pepper and add them to the casserole. Cook over moderately high heat, turning once, until golden, about 7 minutes total. Transfer the chops to a plate.
Add the onion, carrot, celery, garlic and a generous pinch each of salt and pepper to the casserole and cook over moderately high heat, stirring, until the vegetables just start to soften, about 5 minutes. Add the stock, thyme, bay leaves and 2 cups of the milk and bring to a simmer. Return the pork chops to the casserole, cover and braise over very low heat until tender, about 2 hours.
Meanwhile, in a large saucepan, cover the potatoes with water and bring to a boil. Add a generous pinch of salt and simmer over moderate heat until the potatoes are tender, about 20 minutes. Drain. Add the cream and 4 tablespoons of the butter to the saucepan and warm over low heat until the butter is melted. Pass the potatoes through a ricer into a bowl, then stir in the warm cream-butter sauce. Season the mashed potatoes with salt and pepper; keep warm.
Transfer the pork chops to a platter and cover with foil. Spoon 4 cups of the braising liquid and vegetables into a blender, discarding the bay leaves, thyme sprigs and remaining vegetables and liquid. Puree the vegetable sauce until smooth.
In a medium saucepan, melt the remaining 2 tablespoons of butter over moderately high heat. Whisk in the flour and cook until bubbling. Whisk in the vegetable sauce and the remaining 1/2 cup of milk; cook over moderate heat, whisking, until the gravy is thickened and no floury taste remains, about 10 minutes. Season with salt and pepper. Serve the chops with the mashed potatoes and gravy.