Put the trahana in a large bowl and pour in 5 cups of water to cover it well (add more water if necessary). Let it soak for 2-3 hours or better, the night before, if the trachanas is very dry.
Then, put a pot on the fire and pour in the trachana along with all the water in the bowl. Add another 5 cups of water and let it boil. Mix it and then put the pot on the lowest heat and let it simmer for 30 minutes.
From time to time, make sure you stir the mixture to prevent the trachanas from sticking. We want the trachanas to be thick and not watery. Depending on your taste, add the rest of the water.
Next, add the salt, pepper and broth (if you like it) and continue boiling for another 5 - 10 minutes.
Take the soup off the heat, blend it to make a velouté and add the sour cream. Mix well.
Put the olive oil in a pan and brown the halloumi well.
Serve the trahana soup hot with the baked halloumi and garnish with mint leaves.