To make the crust: In the bowl of a stand mixer fitted with the paddle attachment, add the flour, and cane sugar. Turn on low for 2 to 3 rotations to combine the dry ingredients.
Remove butter from the fridge and chop into small cubes, the smaller your cubes are the flakier your crust. I recommend at least cutting the sticks of butter into 4 and then chop into small cubes from there. Add the cold cubed butter to the flour mixture.
Measure out cold water and have ready.
Turn mixer on low, slowly start to incorporate all ingredients. Gradually turn 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 mixer.
Divide dough into six pieces, weighing about 3 ounces (85 grams) each. Form each piece of dough into a disk and place on a baking sheet or individually wrap with plastic wrap if chilling overnight. If on a baking sheet, wrap the sheet with plastic wrap. Allow to chill in the fridge for at least 4 hours or overnight before rolling out pies.
Preheat oven to 350°F. Line 2 baking sheets with parchment paper.
To make the filling: In a medium bowl, add the sugar, flour, cornstarch, honey, and cinnamon and mix together.
Pit and slice the apricots into thin slices. Add the apricots to the bowl with the flour and coat completely. Set aside.
To make the pie wash: In a small dish, add the water and honey. Microwave for 20 seconds to melt the honey so it combines with the water.
On a floured surface remove the plastic wrap from the six dough disks. Roll out to ¼-inch thick, that are about 6-inches in diameter. Transfer to the prepared baking sheets.
Place a generous amount of filling into the middle of each dough, leaving about a 1-inch boarder. Fold the boarder into the middle to create a crust. Using a pastry brush, brush the crust of each mini pie with the honey and water wash.
Bake for 50 minutes or until golden brown. Let cool completely on baking sheets.
To make the glaze: In a small bowl, add the powdered sugar and milk and whisk together until smooth. Drizzle over the top of each pie.
Store in a cool dry place for up to 3 days.