Heat your oven to 100°C/Fan 80°C/Gas ¼. Rinse the pearl barley under cold water, then tip into a pan with the porcini mushrooms. Grate in the zest from the lemon. Pour over 400 ml boiling water and cover. Simmer over a medium heat for 40 mins.
Meanwhile, make your yogurt flatbreads. Tip the flour into a large bowl, saving 1 tbsp for later. Add 1 tsp baking powder and a pinch of salt. Whisk two-thirds of the yogurt in a jug with 3 tbsp cold water. Pour into the flour and knead to a soft, wet dough.
Divide the dough into 4 balls. Flour your hands with the remaining flour and flatten each ball to the size of a saucer. Heat 1 tbsp oil in a large frying pan. Pop 2 flatbreads into the hot oil and cook for 2-3 mins on each side till golden and bubbly. Repeat with the remaining dough. Lay the flatbreads on a plate and put in the oven to keep warm.
Thickly slice the mushrooms, keeping any smaller ones whole. Thinly slice the shallots. Strip the leaves from the thyme. Roughly chop the parsley. Cut the zested lemon into wedges.
Halve the pomegranate across the midde. Holding the halves in your cupped hand, cut-sides down, whack them with a wooden spoon. The seeds should fall out. Catch them in a bowl.
Heat the frying pan you used for your flatbreads over a medium heat. Add 1 tbsp oil, the mushrooms, shallots and thyme. Fry for 4 mins till softened. Pour in 2 tbsp brown rice vinegar and sizzle for 1 min.
The pearl barley should be al dente (soft with a slight bite). Tip it into the mushroom pan with any remaining cooking water. Cook for 5 mins. Taste and season.
Spoon the mushrooms onto the fluffy flatbreads. Dollop on the remaining yogurt. Scatter over the pomegranate seeds and parsley. Serve with the lemon wedges.