Finely grate or pare the zest from the lemon. Juice it. Pick the leaves off half the thyme sprigs. Mix the lemon juice, thyme leaves, 1 tsp cayenne pepper and 1 tbsp olive oil together. Season the marinade.
Pop the chicken in a glass, plastic or ceramic dish (metal will react with the lemon juice). Pour over the marinade. Turn to coat the chicken. Put to one side for 5-10 mins so it can soak up the flavours.
Peel and finely chop the onion. Peel and grate or crush the garlic. Quarter and deseed the tomatoes. Dice the tomato flesh. Break the broccoli into florets.
Warm ½ tbsp olive oil in a pan. Add the onion. Season. Fry for 5 mins till the onion is soft and pale golden. Keep stirring while it cooks.
Stir in the garlic, lemon zest and tomatoes. Fry for 2 mins. Add the bulgar wheat and 250ml boiling water. Bring to the boil. Cover. Lower the heat. Simmer for 8-10 mins till the water is absorbed.
Heat your grill to high. Thread the chicken onto skewers. Grill for 10-15 mins. Turn every so often till the chicken is golden and cooked through.
While the chicken and bulgar wheat cook, bring a pan of water to the boil. Add the broccoli. Boil for 3-5 mins till just tender. Drain. Serve the kebabs with the bulgar wheat and the broccoli.