Wash, clean and roughly grate the zucchini. Peel garlic and chop finely. Heat 2 tablespoons of oil in a frying pan. Fry the zucchini and garlic for 2-3 minutes. Season with salt, pepper and sugar, remove from heat and allow to cool slightly.
Let the dough sheets rest at room temperature for about 10 minutes. Whisk yoghurt, 100 ml oil, 200 ml milk and eggs together, season with a little salt. Mix 50 ml milk and 5 tbsp. oil. Coarsely grate the feta, mix into the zucchini mixture.
Spread a damp cloth over the work surface and place a dry one on top. Roll out the dough sheets on the cloths. Spread with the oil-milk mixture. On the lower long side of each pastry sheet, spread some zucchini mixture in a long strand.
Roll up, place in spiral form in a greased casserole dish. Pour the yoghurt mixture evenly over the top.
Bake in a preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: see manufacturer) for approx. 40 minutes until golden brown. Wash parsley and dab dry. Pluck leaves and chop finely. Remove the borek from the oven and sprinkle with parsley.