Combine sugar, water and yeast in a jug. Stand for 10 minutes.
Place flour and salt in a large bowl. Add yeast mixture and milk and combine to make a soft dough. Turn onto a lightly floured board and knead gently until smooth. Divide dough into four portions. Place on a lightly floured board, cover with plastic and stand in a warm place for 20 minutes or until dough has doubled in size.
Meanwhile, heat half of the oil in a large non-stick frying pan over medium heat. Add onion and garlic and cook, stirring often for 5 minutes or until onion is soft.
Increase the heat to high, add mince, cumin and oregano and cook, stirring to break up the lumps, for 10 minutes until browned. Transfer to a bowl. Cool 5 minutes, add parsley and mint.
Heat remaining oil in same frying pan. Add the mushrooms and cook a further 5 minutes or until browned lightly. Remove from heat.
On a lightly floured surface roll dough into a 30cm x 40cm rectangle. Place one-quarter of the mince mixture, mushrooms and feta on one half of each rectangle season with salt and pepper. Fold dough over to enclosed filling. Press edges together to seal.
Preheat a barbecue plate or frying pan on medium until hot.
Brush both sides of dough with oil and cook, for about 3 minutes or until golden, then turn and cook for a further 3 minutes. Serve with lemon wedges.