Place blackberries (and cinnamon stick, if using) in a dry saucepan and cook over medium heat. Cook until the berries soften and release their juice. Mash them down with a spoon to help them break up.
Once blackberries are bubbling and the juice is released (roughly 5-10 minutes) turn off the heat and empty everything into a strainer placed over a bowl and drain off the juice. Mash them down to get as much juice as possible.
Return the juice to the saucepan and place over a low heat. Now add honey, one spoonful at a time and dissolve well. Taste after adding 3 tablespoons and stop adding when it seems sweet enough. When sauce coats the back of a spoon it’s nearly ready.
Add lime juice, stir through and turn off the heat. Decant the sauce into a jar to cool. Will keep in a glass jar in the fridge for at least a week. Enjoy mixed into some natural yogurt (pictured here, with blueberries).