In a saucepan over medium heat add blackberries, salt, and sugar. Cook until the blackberries start releasing their juice. While the blackberries are cooking mix 1½ tablespoons of the lemon juice with the cornstarch to make a slurry. Once the blackberries have been cooking for about 4-5 minutes add the cornstarch mixture and cook until the compote thickens. Set aside and allow to cool to room temperature.
While the compote is cooling roll out the dough to a 12" x 18" rectangle. Cut into 6 equal squares and place on the lined sheet pan.
Spoon the blackberries into the middle of each of the squares and fold in half along the diagonal. Seal the edges using a fork. Then poke a hole in the top of the turnover. Mix the egg yolk with a tablespoon of milk and brush over the tops of the turnovers.
Bake for 20 - 30 minutes or until the crust is a golden brown.
While the turnovers are cooling mix the remaining ½ tablespoon lemon juice, 1 tablespoon of milk, and powdered sugar. When the turnovers have cooled drizzle the icing over the top.