Preheat the oven to 200°C fan.
First, make the dough for the flatbreads. Put the flour, yeast, oil and ½ teaspoon of salt into a large bowl. Pour in the water and use a spatula to combine the mixture. Transfer to a lightly oiled work surface and then, with lightly oiled hands, knead the dough for 5 minutes until it's soft and elastic. You may need to add more oil if the dough starts to stick to your work surface. Return to the bowl, cover with a slightly damp clean tea towel and leave to rise in a warm place for at least 1 hour (preferably 2 hours), until nearly doubled in size. Cut the dough into four equal pieces and set aside.
While the dough is rising, make the garlic butter. Drizzle the head of garlic with 1 teaspoon of oil and sprinkle with a little salt and pepper. Wrap tightly in foil and bake for 40 minutes, until the cloves have softened. Remove the foil and when cool enough to handle, squeeze out the cloves, discarding the papery skin. Increase the oven temperature to 240°C fan.
Put the cooked, raw and black garlic into a pestle and mortar with 1½ teaspoons of flaked salt and a generous grind of pepper. Pound to a rough paste, then transfer to a bowl with the parsley, caraway seeds and softened butter. Mix everything together and set aside.
Coarsely grate the tomatoes, discarding the skin. Transfer the tomatoes to a sieve set over a bowl and set aside to drain a little.
Place a large baking tray on the middle shelf of the oven to heat up.
Transfer the dough balls to a lightly oiled work surface and use your hands to stretch each piece into a rough circle, about 18cm wide and ½cm thick.
Bake two flatbreads at a time. Remove the hot tray from the oven and quickly place each flatbread on the tray, spaced apart. The dough will be very thin but should have enough elasticity not to break. If you do get a hole in the dough, don’t worry; this just adds to the homemade look.
Quickly return the tray to the oven for about 7–8 minutes, until the dough is golden-brown and crisp. Continue with the other two flatbreads in the same way.
Spread each flatbread with about 1 tablespoon of the garlic butter and top with the drained, grated tomatoes and the black garlic slices. Sprinkle over the herbs and finish with a drizzle of oil, a generous pinch of flaked salt and a good grind of pepper.
