Combine blackberries, sugar, 2 cups water, butter, and cinnamon in a saucepan. Simmer for 25 minutes.
In a bowl, mix flour and salt. Cut in shortening until crumbly.
Add egg yolk and milk (one tbsp at a time) until a dough ball forms.
Shape dough into small balls or flat strips.
Drop dough into the simmering berries. Cover and simmer for 15 minutes without stirring.
Remove cooked dumplings to a plate.
Whisk cornstarch and 1/2 cup water; stir into the berry juice.
Boil sauce until thickened, then pour over dumplings.