Preheat oven to 375 degrees F (190 degrees C). Lightly grease a cookie sheet.
Mix the cream cheese, sugar, and cinnamon together in a bowl until thoroughly blended. Set aside.
Place the puff pastry shells on the prepared cookies sheet. Brush each shell with milk and sprinkle with turbinado sugar.
Bake in preheated oven until shells expand and turn golden brown, 10 to 15 minutes. Watch closely to make sure shells bake thoroughly, but do not overbake. Remove shells from oven, and use a fork to remove the cap from each shell. Set the caps aside.
Spoon 2 tablespoons of the cream cheese mixture into each shell. Top with 6 to 8 blackberries. Place a puff pastry cap on top of each shell over the berries.
Return filled pastry shells to oven, and bake until pastry tops are golden brown and the filling is warm, about 5 minutes more.