To make yoghurt dressing, whisk tahini, lemon zest and juice and oil until smooth. Whisk in remaining ingredients. Season.
To make bread, place yoghurt and beer in an electric mixer fitted with a dough hook. Mix on low to combine. Add flour and salt. Mix to form a soft dough. Turn dough out onto a floured surface and knead for 2 minutes until smooth. Divide dough into 8 portions. Roll each portion on a floured surface into a 5mm thick rectangle. Set aside.
To make lamb and ale filling, heat half the oil in a medium saucepan over medium heat.
Cook mushrooms until tender and all liquid has evaporated. Remove from pan and set aside.
Add remaining oil to same pan. Cook onion and garlic until soft. Add spices and cook, stirring, for 2 minutes. Add tomato paste and cook, stirring for 2 minutes. Add mince and cook, breaking up meat, for 5 minutes or until browned. Stir in beer and pine nuts. Season. Add cooked mushrooms. Bring to a boil. Reduce heat and simmer, covered, stirring often, for about 30 minutes or until mixture is thickened, reduced and flavoursome. Cool.
To assemble, place flatbreads on bench and spoon lamb filling into centre. Top with tomato, onions, parsley and mint. Fold two long sides into the centre to overlap. Pinch two short sides closed to seal.
Heat oil and garlic in a large frying pan over low heat to infuse garlic for 5 minutes. Add gozleme, seam-side down and cook, turning, until browned all over and bread is cooked through.
Serve gozleme with yohgurt dressing and lemon wedges.