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Heat oven to 200C/180C fan/gas 6. Heat 1 tbsp oil and the butter in a large ovenproof frying pan or wide flameproof casserole dish. Season the chops generously and fry over a medium-high heat for 3 mins each side until lightly golden – brown the edges of the fat for 30 secs or so too. Remove to a plate.
Add the sliced shallot and fennel to the pan and cook for 2 mins, stirring now and then. Splash in the wine and simmer for a few secs to reduce a little. Add the lemon wedges, drizzle with the remaining oil and put in the oven to roast for 10 mins.
Toss the veg gently, sit the pork chops on top and roast for another 20 mins. Add the tomatoes to the pan and cook for 5 mins more or until the chops are cooked through, the fennel is tender and turning golden, and the tomatoes are soft.
Meanwhile, mix the chopped shallot, the lemon juice, beans and fennel seeds. Remove the meat to a plate to rest for a few mins while you fold the dressed beans and basil leaves into the pan. Add the resting juices, season to taste, then serve with the pork.