for the crust
2 1/2 cups all purpose flour
1 tablespoon sugar
3/4 teaspoon salt
10 tablespoons (1 1/4 sticks) chilled unsalted butter, cut into 1/2-inch pieces
1/3 cup chilled solid vegetable shortening, diced
6 tablespoons (or more) ice water
for the filling
3/4 cup + 2 teaspoons cup granulated sugar, divided
1 tablespoon cornstarch
3/4 teaspoon salt
5 egg yolks
1 3/4 cups buttermilk
1/4 cup heavy cream
4 tablespoons unsalted butter, melted
2 teaspoons distilled white vinegar
1 1/2 teaspoons vanilla extract
1 cup fresh blueberries
Blend flour, sugar and salt in processor. Add butter and shortening and cut in using on/off turns until mixture resembles coarse meal. Add 6 tablespoons ice water and process until moist clumps form, adding more water by teaspoonfuls if dough is dry. Gather into ball, then flatten into disk. Wrap in plastic; chill 2 hours.
Roll the dough into a 12-inch circle on a lightly floured surface. Transfer the dough to a pie plate and fold any overhanging dough underneath itself so the edge of the dough is flush with the outer edge of the pie plate. Crimp edges as desired. Refrigerate the dough-lined pie plate for 40 minutes, then place in the freezer for 20 minutes. While the crust is in the freezer, preheat oven to 375F.
Line the chilled pie plate with two pieces of parchment paper, allowing the parchment edges to hang over the edges of the pie crust. Fill the lined pie crust with pie weights, place on a lined baking sheet and bake on the lower-middle oven rack until lightly golden around the edges, 20 to 25 minutes. Remove the parchment and pie weights, rotate the baking sheet and continue to bake until the crust is golden brown, 5 to 7 more minutes. Brush the surface of the hot crust with the egg white and bake for an additional 1 minute.
While the crust is baking, prepare the pie filling. In a large bowl, whisk together the 3/4 cup of sugar, the cornstarch and salt. Add the eggs and egg yolks and whisk to thoroughly combine. Add the buttermilk, heavy cream, melted butter, white vinegar and vanilla extract, and whisk until completely combined.
Once the crust is done, reduce the oven temperature to 300F. If the pie filling has been sitting for a few minutes, give it a short whisk to recombine. Leaving the pie crust in the oven (just slide the oven rack out a bit), carefully pour the filling into the hot pie shell. Sprinkle in the blueberries. Bake for 10 minutes.
Again, leaving the pie crust in the oven and just sliding the oven rack out, sprinkle the remaining 2 teaspoons of sugar evenly over the top of the pie. Continue to bake until the center jiggles very slightly when the pie is shaken, 30 to 40 minutes. Remove the pie from the oven and increase the oven temperature to 450 degrees F. Once the oven comes to temperature, place the pie on the upper-middle rack and bake until the top is golden brown, 5 to 7 minutes.
Remove from the oven and place the pie plate on a wire rack and allow to cool for 30 minutes. Transfer the pie to the refrigerator and chill for at least 3 hours before serving.