Place in the bowl of a mixer the butter and start beating it. Slowly add the oil to get well incorporated. Then add one by one the eggs and continue beating at medium speed.
Mix the yoghurt with the baking powder and add it to the mixture. Then add the halloumi and the feta along with the mint at a slower speed.
Pour some of the milk and some of the flour and mix, while repeating this process.
In the meantime, turn the oven to 175°C, air circulation, rack set at the middle.
Use an oven proof rectangular baking form and brush it with some butter or oil. Pour the mixture in it and sprinkle the sesame seeds on top. Place in the preheated oven and cook for about 1 hour.