Cut the tomatoes in half horizontally and carefully remove the seeds. Sprinkle the cut sides with salt and place cut-side down on kitchen paper to remove some liquid. Leave to stand for 20 minutes. Rinse and pat dry with kitchen paper.
Preheat the oven to 200C/400F/Gas 6. Place the shallot in a food processor with the garlic, thyme leaves, oil and anchovies and then blend to a smooth paste. Transfer to a bowl and fold in the parsley, chilli flakes and breadcrumbs until well combined. Season to taste.
Spoon the bread mixture into the tomato cavities and bake for about 15 minutes until bubbling and golden. Transfer to a dish and serve hot or at room temperature, drizzled with extra virgin olive oil and balsamic vinegar.