To make the crust: In the bowl of a stand mixer fitted with the paddle attachment, add the flour and cane sugar. Turn the mixer on low for two to three rotations to combine the dry ingredients.
Remove the butter from the fridge and chop into small cubes. The smaller the cubes, the flakier the crust. Cut the stick of butter into four and then chop into small cubes from there. Add the cold, cubed butter to the flour mixture. Measure out the cold water and have it ready.
Turn the mixer on low and slowly start to incorporate the ingredients. Gradually turn the mixer to medium speed. Once the butter mixture looks like wet sand, immediately add in all the water. As soon as the dough comes together, stop the mixer. Do not over mix.
Divide the dough into two portions, one should be almost double the size of the other. I prefer to weigh them, the large one should weigh 312 grams and the small should weigh 170 grams. Form them both into disks and wrap separately in plastic wrap. Allow to cool in the fridge for at least 6 hours or overnight.
Preheat the oven to 350°F.
To make the filling: In a large bowl, add the cane sugar, flour, and cornstarch and whisk together. Add the apples, strawberries, and blackberries and fold together with a spatula to coat the fruit completely. Set aside.
To make the topping: Add the heavy whipping cream to a small dish.
Grease a 9-inch pie pan well with butter. Remove the pie dough from the fridge. Remove the plastic wrap and place on a floured surface. First, roll out the large disk to ¼-inch thick, it should be about 11-inches in diameter. Place the pie dough into the pie pan, and press lightly to form against the pan. It should be large enough that the dough folds right over the top. Roll out the smaller disk to ¼-inch thick, it should be about 9-inches in diameter. Set aside.
Add the filling into the pie pan and spread evenly.
Cut the top pie crust into strips that are about 1-inch thick. Reserve the shorter pieces for the edges of the pie and the larger pieces for the middle.
Lay them over the top of the pie with about 1-inch in-between. Then pull back every other strip of dough, then lay a strip down perpendicular to the ones you just laid. Pull back every other strip, opposite of what you just did, and lay another strip 1-inch apart horizontal to the strip you just laid. Continue doing this until the pie is completely covered.
Trim off an extra pie dough that hangs over the edge of the pie pan. Crimp the two together, and then roll the pie crust twice to create an edge that seals the filling in. Flute the edges by using your thumb and index finger of your right hand to pinch the rolled edge of dough and push your index finger of your left hand into it to create the “flute”. Continue around the entire pie to flute the edges.
Using a pastry brush, brush the dough with the heavy whipping cream. Sprinkle the top with turbinado sugar.
Bake for 1 hour and 15 minutes, or until golden brown.
Store at room temperature for up to 3 days.