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.
To make the filling: In a small saucepan, add the apples, cane sugar, honey, lemon juice, flour, cornstarch, and cinnamon and mix together. Put over medium heat, and continue to stir occasionally. The sugar will start to melt and coat the apples. The juices will start to bubble. Continue to cook until the liquid has thickened, you’ll know when you scrape the bottom of the pot and you can visibly see that it doesn’t fill in the open space immediately. This should take 8 to 14 minutes. Place the mixture in the fridge to cool, or allow to cool until room temperature.
Preheat the oven to 350°F.
To make the topping: Add the honey and water to a small dish. Microwave it for 10 seconds or so to melt the honey so you can completely stir it together. Set aside.
Grease the 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.
I like to use a pizza cutter for this next step, but a sharp knife will work as well. Cut the rolled out dough into 1-inch wide strips. Place the strips on top of the apples going horizontal leaving 1-inch between strips. Use the smaller strips towards the sides of the pie and use the longer strips for the middle. Next, add the remaining dough strips going vertical, alternating each strip over and under the horizontal ones.
Once the lattice top is complete, crimp and fold over the edges of the dough to seal the top and bottom together. Flute the edges. Using a pastry brush, brush the dough with the water and honey topping.
Bake for 1 hour and 15 minutes, or until golden brown.
Store at room temperature for up to 3 days.