In a saucepan add the sugar, lemon juice, lemon zest, strawberries, blackberries, and blueberries. Over medium high heat bring the filling mixture to a boil. The berries will release a lot of water. Cook until the liquid reduces by half.
While the filling is cooking mix the cornstarch with 2 tablespoons of water to create a slurry. Pour the slurry into the filling. Allow to boil and cook for 3 minutes the remove from the heat.
Place the filling in a metal bowl and place into an ice bath to help cool quickly.
Making the turnovers
Preheat the oven to 400°F, 200°C, or gas mark 6.
When the filling is almost done cooling (it only has to get to around room temperature) slice the puff pastry into 8 equal squares.
Spoon about 2 tablespoons of filling onto the middle of each pastry square. Fold in half on the diagonal and use a fork to seal both sides. Place the turnovers on a sheet pan lined with parchment paper or a silicon mat.
Whisk the egg and milk together and brush over the top of each turnover. Sprinkle with turbinado sugar and bake for 12-15 minutes or until the dough is a nice golden brown.
Allow to cool completely before eating the filling can burn your mouth.