Prepare the cheese: The process for the filling starts two days before we make the Flaounes. Grate the cheese using the fine side of a grater and place them in a bowl. Do the same for the halloumi. Cover them with plastic wrap and put them in the fridge. Occasionally, mix the cheeses, bringing the top ones down to the bottom. This way, they will dry out and absorb more eggs, resulting in fluffier Flaounes.
Prepare the Flaounes: On the day we make the Flaounes, we take the cheese and halloumi out of the fridge to bring it to room temperature.
Make the dough: Pour the lukewarm water and milk into a bowl and add the yeast. Stir and set aside for 20 minutes.
We put the flour, salt, mahlepi, mastic, sugar in the mixing bowl and mix with the hook. Add the oil and mix. Gradually add a little quantity of the milk and a little of the lightly beaten eggs until the dough is soft and does not stick to our hands. Knead it in the mixer for 5 minutes. By hand, we need to knead for 10 - 15 minutes. Shape the dough into a ball, coat it with some oil, and cover it with a towel and then a blanket. Let it double in volume, which will take about 1 ½ hours.
For the filling: In a bowl, add the cheese, halloumi, mastic, sugar, flour, baking powder, raisins, and mint, and stir well. Then, gradually add the lightly beaten eggs, little by little. To have the filling ready, we need to form a large ball, squeeze it with our palms, and make sure it doesn't break. We need to be careful when adding the eggs because the mixture may not be able to handle them all. Cover the bowl with a towel, and then with a blanket.
Place non-stick baking paper onto two baking pans and preheat the oven to 180°C on Fan. Take 160g of the filling and form a tight ball. We will make a total of 15 balls of 160g.
Shape the dough into a long stick and cut it into 15 pieces of 110g. Shape 15 small balls of dough and cover them with a towel. Take a ball of dough and open it with the rolling pin into a thin sheet, about 3mm thick. Using a dessert plate (about 16cm in diameter) as a guide, cut round discs from the sheet.
Mix the sesame seeds a little and put the sheet inside, pressing it to stick to the bottom. Open it slightly with the rolling pin to make the sesame stick well. Put a ball of filling in the centre. Bring the top and bottom sides towards the centre of the filling.
Press the bottom of the filling to secure the sheet. Fold the opposite sides inward and press with your fingers to secure the sheet. If we want, we press the corners of the Flaouna with a fork. We place them in the baking pan, leaving 3 cm between them, and brush them (the sheet and the filling) with the beaten egg (if desired, we also add a little sesame inside). We bake the Flaounes in a preheated oven for 45-50 minutes or until they become golden-browned.