Heat the olive oil and butter in a large pot over a medium heat. Once the butter is melted add the onion and leeks and cook until softened, about 10 minutes. Add the flour and stir into the mixture, allow to cook for a couple of minutes.
Stir in the milk and chicken stock then throw in the broccoli, carrot, bay leaves, thyme and nutmeg. Cook until the broccoli is soft, probably about 25 minutes.
Once it's done blend the soup up in batches. It doesn't need to be completely smooth, just get it to the consistency you like. Return it to the heat and stir in the grated cheese.
To Make the Halloumi Fries
Pour olive oil into a saucepan so that it comes up the sides a couple of inches. Heat over a medium high heat. Mix the flour and whichever spice you've chosen on a plate then dredge each piece of halloumi so that it's coated on all sides. Place the halloumi pieces in the hot oil and cook for a couple of minutes on each side. You might need to do this in batches depending on the size of the pan. Remove the halloumi fries and place on a piece of kitchen towel to drain. Serve with the soup and do lots of dipping!