Crack the egg into a bowl and beat with a fork. Tip in the mince. Peel and grate in the garlic clove. Sprinkle in 1 tsp cinnamon and plenty of salt and pepper. Use your hands to mix and squeeze everything together. Divide into 4 flattish burgers. Pop on a plate. Cover with cling film and chill while you get everything else ready.
Tip the bulgar wheat into a pan and cover with 150ml boiling water. Simmer on a gentle heat for 10-15 mins till the water has been absorbed. Set to one side to cool slightly.
While the bulgar wheat cooks, crumble 100g feta into a small bowl. Add the yogurt. Zest in the lemon and add a good crack of black pepper. Stir together with a fork. Set aside.
Squeeze the lemon juice into a separate bowl. Peel and thinly slice the onion. Add to the juice. Toss to coat. Cut 1/2 the cucumber into small cubes and add to the bowl (don’t stir). Finely chop the mint leaves and scatter them in. Wash, dry and tear the leaves from 1/2 the lettuce. Pop in the bowl.
Chop the tomatoes into wedges. Slice the aubergine into rounds approximately 1cm thick. Brush them with 1 tbsp oil.
Heat your grill to high. Pop the burgers on a rack resting on a foil-lined baking tray. Grill the burgers for 6-8 mins till golden brown. Flip and grill for another 6 mins till cooked through.
While the burgers are cooking, set a griddle pan or heavy-based frying pan over a medium heat to warm for a few mins. Add the aubergine slices and cook for 3-4 mins on each side till softened, golden and slightly charred. You may need to do this in batches. Once the aubergines are cooked, add the tomatoes to the pan. Fry for 2 mins till they are just softened and charred. Take off the heat.
Assemble the burger stacks. Place a couple of aubergine slices on each plate. Perch a burger on each. Top with 1 tsp whipped feta. Add a tomato wedge. Top with another aubergine slice to finish.
Add the remaining tomatoes and aubergines to the bowl of salad. Fold in the bulgar wheat with 1 tbsp olive oil. Serve the burgers with the salad and the remaining whipped feta on the side.