Wash the tomatoes and halve them as desired. Wash the potatoes thoroughly and cut them in half lengthwise. Wash thyme, shake dry and pluck off the leaves. Mix tomatoes, potatoes, thyme, salt, pepper and 5 tbsp. oil well.
Preheat oven (electric cooker: 200 °C/recirculating air: 175 °C/gas: see manufacturer). Wash chops and pat dry. Heat 2 tablespoons of oil in a large pan. Brown the meat in it in 2 portions on each side.
Season with salt and pepper. Place in a large casserole dish.
Spread the tomato and potato mixture in the pan and drizzle with the frying fat from the pan. Braise in the hot oven for approx. 1 1⁄2 hours until the meat can be easily removed from the bone. After about 1 hour, cover with aluminium foil if necessary.
Serve sprinkled with coarse sea salt.