1. The process for the filling starts two days before making the flaounes. Grate the cheese on the fine side of the grater and place it in a bowl. Do the same with the halloumi. Cover them with plastic wrap and refrigerate. Occasionally, stir the cheeses, bringing the bottom ones to the top. This way, they will dry out and 'absorb' more eggs, resulting in fluffier flaounes.
Preparing the Flaounes:
1. On the day you make the flaounes, take the cheese and halloumi out of the fridge to come to room temperature.
Making the Dough:
1. Pour the lukewarm water and milk into a bowl and add the yeast. Stir and set aside for 20 minutes.
2. In the mixer bowl, add the flour, salt, mahlepi, mastic, and sugar, and mix with the dough hook. Add the oil and mix. Gradually add a small amount of the milk and a small amount of the lightly beaten eggs until you form a soft dough that does not stick to your hands.
3. Knead in the mixer for 5 minutes. By hand, you should knead for 10 - 15 minutes. Shape the dough into a ball, brush it with a little oil, cover it with a towel, and then with a blanket. Let it double in volume. This will take about 1 ½ hours.
For the Filling:
1. In a bowl, combine the cheese, halloumi, mastic, sugar, flour, baking powder, raisins, and mint, and mix well. Then, gradually add the lightly beaten eggs. For the filling to be ready, you should be able to form a large ball, squeeze it with your palms, and it shouldn't break. Be very careful when adding the eggs as it might not absorb all of them. Cover the bowl with a towel and then with a blanket.
2. Line 2 oven trays with non-stick baking paper and preheat the oven to 180°C (350°F) on fan mode. Take 160g of the filling and form a firm ball. You will form a total of 15 balls weighing 160g each.
3. Roll the dough into a long rope and cut it into 15 pieces weighing 110g each. Form 15 dough balls and cover them with a towel. Take one dough ball and roll it out with a rolling pin into a thin sheet about 3 millimeters thick. Using a small saucer (about 16 cm in diameter) as a guide, cut round discs from the sheet.
4. Lightly mix the sesame seeds and dip the bottom side of the dough disc into them, pressing so they stick. Roll it slightly with the rolling pin to ensure the sesame adheres well. Place a ball of filling in the center. Bring the top and bottom edges towards the center of the filling. Press the dough at the bottom part of the filling to secure it.
5. Fold the opposite sides inwards and press with your fingers to secure the dough. If you wish, press the corners of the flaouna with a fork. Place them on the tray, leaving 3 cm between them, and brush them (the dough and the filling) with the beaten egg (if you like, add some sesame seeds on top too). Bake the flaounes in the preheated oven for 45 - 50 minutes or until nicely golden brown.