Heat oven to 180C/160C fan/ gas 4. Put the oil and butter in a large saucepan over a medium heat. Add the onion, garlic, celery, carrot, anchovies and chilli flakes, and cook for 10 mins.
Add the tomato purée and tomatoes, and turn the heat up until bubbling. Allow to bubble for 10 mins, stirring frequently to ensure it doesn't stick.
Add the capers, sugar, 1 tsp salt and a good grind of black pepper. Bubble for 25 mins more until the sauce has reduced.
Take off the heat, stir through most of the herbs, then transfer to a baking dish. Halve the artichokes and nestle these in the sauce. Top with the cheese and pine nuts, and bake for 25-30 mins until golden brown and bubbling on top. Scatter with herbs before serving.