Combine blackberries, sugar, water, butter, and cinnamon in large pot. Cook over medium-low heat 20-30 minutes, stirring occasionally, until berries break down into thick sauce.
Meanwhile, whisk flour and salt in bowl. Cut in shortening with pastry cutter or two knives until mixture looks like coarse crumbs.
Stir in egg yolk. Add milk one tablespoon at a time, mixing with fork, until dough can be squeezed into a ball. Stop adding milk as soon as dough holds together.
Divide dough in half. On floured surface, roll each half to 1/4-inch thickness.
Cut rolled dough into strips 2-3 inches wide.
When berry mixture is boiling, hold each strip over pot and pinch off 4-inch pieces, dropping them into the bubbling berries. Continue until all dough is used.
Reduce heat to medium. Cook 15 minutes without stirring. May gently push dumplings down into liquid but do not stir or they will fall apart.
Remove from heat and let rest 10 minutes to thicken before serving.