Method
Prepare your fire. It needs to be moderately hot, with a large bed of glowing embers.
Set a grill over the fire; the temperature is right when you can hover your hand over it for a maximum of 4 seconds. Place the onion halves, cut side up, on the grill. Season with salt and pepper and trickle on a little olive oil. Cook for 15–20 minutes or until they are beginning to soften. Now turn them over and cook on their cut side for a further 15–20 minutes. Set the onions to one side; keep warm.
Place the trimmed broccoli in a large bowl, trickle with 2 tbsp olive oil and season with salt and pepper.
Stoke the fire and feed it if necessary – you want it fiercely hot now, so that you can hover your hand over the grill for 2 seconds at most. Arrange the broccoli over the grill and cook it for 4–5 minutes until beginning to soften and char around the edges. Move the broccoli to one side.
Lay the cheese on the grill and scatter over the thyme leaves, if using. Cook for a couple of minutes on each side or until golden and charring in places.
Transfer the hot broccoli to a warmed platter. Peel the charred skin from the onions and arrange the soft centres over the broccoli. Add the halloumi and give everything a final trickle of olive oil and vinegar. Serve with warm grilled sourdough.