Place blackberries, sugar, water, butter and cinnamon in a large saucepan. Cook and stir occasionally over medium heat until have started to break down and form a sauce, about 20 to 30 minutes.
Meanwhile whisk together the flour and salt in a mixing bowl. Cut in the copha with a knife or pastry blender until the mixture resembles coarse crumbs. Stir the egg yolk into the crumbs.
Add the milk a tablespoon at a time, tossing with a fork until the flour mixture is moistened. Do not add more milk than you need: when you squeeze a handful of the moistened pastry mixture it should form a ball. Divide the dough in half and shape into balls.
Roll one ball into a 5mm thick round, like a pie crust. Using a floured knife cut lengthwise 5cm wide squares of dough. Repeat with the second ball of dough.
Drop the dumplings one by one into the berries. Repeat until all the dough has been used. Cook the dumplings over medium heat for 15 minutes. You may push the dumplings down into the juice but do not stir until they are fully cooked or they will clump together.