Preheat oven to 450 degrees F.
Thaw the sheets of puff pastry as per the box instructions.
Peel and core the apples and cut into quarters. Toss the apples in the lemon juice so they do not brown while you are dicing them. Cut each quarter into about 2 to 3 (1-inch) pieces.
In a large saute pan over medium heat, melt the butter until lightly browned. Add the apples and saute for about 3 to 5 minutes until lightly browned. Add the honey and a pinch of salt and toss to mix in well, transfer to the oven and roast for about 15 minutes until apples are soft. Mash with a fork while still warm. Let the apples cool to room temperature and gently fold in the berries.
Turn the oven down to 400 degrees F.
In a small mixing bowl beat 1 egg. In another small bowl, mix together the cinnamon and sugar.
Lay the thawed puff pastry sheets out flat on a floured work surface. Cut large circles out of the pastry with a ring cutter, about 4 per pastry sheet. Brush with the egg-wash on the outer edge of half of the circle. Spoon 2 tablespoons of the apple berry mixture in the center of each round of pastry dough. Fold the dough over to cover the filling, making a semi-circle and sealing the edges.
Place pies on a buttered oven tray. Repeat with the rest of the pastry dough. When all of the pies are on a sheet tray cut air holes in the top of each pie and brush the tops with egg wash. Sprinkle with the cinnamon sugar. Bake for about 20 to 25 minutes until puffed and nicely browned.
Recipe courtesy of Michael Chiarello