Preheat the oven to 240C/475F/Gas 9. Oil a shallow roasting tin with 2 tbsp of the oil.
Cut the tomatoes in half lengthways and lay them cut-side up in the tin.
Sprinkle over the thyme and some salt and pepper and roast for 15 minutes.
Reduce the oven temperature to 150C/300F/Gas 2 and roast for a further 1½ hours until they have shrivelled to about half their original size and concentrated in flavour. Leave to cool.
Arrange the tomatoes and the feta among four plates and drizzle over the remaining olive oil.
Sprinkle with a bit more sea salt and some black pepper to serve.