Let the filo pastry rest at room temperature for about 10 minutes. Clean, wash and coarsely grate the zucchini. Peel garlic and chop finely. Heat 2 tablespoons of oil in a frying pan. Sauté zucchini and garlic for 2-3 minutes.
Season with a little salt, pepper and 1 pinch of sugar, remove from heat and allow to cool slightly.
Whisk yoghurt, 100 ml oil, 200 ml milk and eggs. Season with salt. Crumble feta coarsely, mix into the zucchini mixture.
Preheat oven (electric cooker: 200 °C/circulating air: 175 °C/gas: see manufacturer). Grease an ovenproof dish. Mix 5 tablespoons of milk and 5 tablespoons of oil. Spread a damp tea towel on the work surface and place a dry one on top.
Roll out the dough sheets. Place the sheets one after the other on the cloths and brush each sheet with some milk-oil mixture. Spread some zucchini mixture on the bottom in a long strand.
Lift the dough a little on this side and fold in the side edges. Roll up the dough using the cloth. Roll to the end with your hands. Form each roll of dough into a snail and place in the casserole dish.
Pour the yoghurt mixture evenly over it. Bake in a hot oven for about 40 minutes until golden brown. Wash parsley, dab dry, pluck leaves and chop finely. Remove the borek from the oven and sprinkle with parsley.