Place a rack in the center of your oven and preheat to 400°F / 200°C.
Place the 5 portions of coconut oil in a small bowl and freeze for 10 minutes until mostly solid.
To make the crust, pulse the flour and salt in a food processor to combine.
Add the chilled coconut oil and pulse until the mixture resembles coarse sand with some pea-sized pieces remaining.
While pulsing, add the ice water 1 Tbsp (15 ml) at a time until the dough just sticks together when pressed between your fingers.
Transfer the dough to a large piece of plastic wrap, form it into a ball, and press into a disk.
Wrap tightly and refrigerate for 30 minutes.
Once chilled, unwrap the dough onto a flour-dusted surface. Lightly flour the top of the dough and a rolling pin, and roll it out into a 12-inch circle about 1/8-inch thick.
Carefully transfer the dough to a 9-inch pie pan. Press it into the pan and flute the edge with your fingers. If the dough separates, simply press it back together.
For blind baking, place a piece of parchment paper over the pie shell and fill it with dried beans or pie weights.
Place on a baking sheet and bake for 10 minutes.
Carefully remove the parchment and beans.
Continue baking the crust for another 10 minutes, or until the shell is lightly golden brown.
Transfer to a wire rack to cool.
Reduce the oven temperature to 350°F / 177°C and move the oven rack to the lower third position.
While the shell cools, make the filling.
In a large bowl, beat the egg and egg whites.
Add all remaining filling and whisk until smooth.
Place the cooled crust (still on its baking sheet) on the oven rack and pour in the filling.
Bake for 45 to 50 minutes, until the edges of the filling are set but the center is still slightly loose.
Transfer the pie to a wire rack to cool completely before slicing and serving.
Patch It Up: Don't worry if your whole wheat dough cracks a bit when transferring it to the pan. It's less pliable than white flour dough. Simply press any cracks back together or patch with a small piece of extra dough.
