Process ¾ cups flour, salt, and sugar together in food processor until combined. Add butter and shortening and process until homogenous dough just starts to collect in uneven clumps, about 10 seconds. Scrape down the bowl with a rubber spatula and redistribute dough evenly around processor blade. Add remaining ½ cup flour and pulse until mixture is evenly distributed around bowl and mass of dough has been broken up, 4 to 6 quick pulses. Empty into a medium bowl.

Sprinkle vodka and water over mixture. With rubber spatula, use folding motion to mix, pressing down on dough until dough is slightly tacky and sticks together. Flatten dough into 4" disk. Wrap in plastic wrap and refrigerate at least 45 minutes or up to 2 days.

Adjust oven rack to lowest position, place rimmed baking sheet on oven rack, and heat oven to 425Roll the dough out on a lightly floured work surface (I like using a Silpato a 12" circle about ⅛" thick. Place a deep 9" round pie plate on top (top side down), then invert the pie crust into the pan, leaving at least 1" overhang on each side. Gently peel the Silpat off the crust. Gently lift the edge of the dough, then it fall into the pan and fit the bottom and sides of the pan (you can press/nudge it into place). Leave overhanging dough in place; refrigerate until dough is firm, about 30 minutes.

Trim overhang to ½" beyond lip of pie plate. Fold overhang under itself; folded edge should be flush with edge of pie plate. Flute dough to flatten it against rim of pie plate. Refrigerate until firm, about 15 minutes.

Line the crust with foil, and fill with pie weights or beans. Bake for 15 minutes.

Remove the foil and pie weights. Brush the egg white on all of the crust, then bake again for 1 minute to set the egg white. Cool completely.

Place the pre-baked pie shell on a rimmed baking sheet and set aside.

In a large bowl, sift together the sugar, flour, salt, and matcha powder. Stir in the butter, then the eggs one at a time, stirring well after each addition. Mix briskly until the filling is thin and light colored. Stir in the cream and half and half, followed by the vanilla.

Strain the filling through a fine-mesh sieve directly into the pie shell. Bake at 325F on the middle rack of the oven for 40 to 50 minutes, rotating 180 degrees when the edges start to set, about to 35 minutes into baking. The pie is finished when the edges are set and puffed slightly and the center is no longer liquid but still wobbles slightly. Be careful not to over-bake or the custard can separate; the filling will continue to cook and set as it cools. Allow pie to cool completely on a wire rack, 3 to 4 hours.

Whip the cream until soft peaks form. Add most of the zest, leaving a pinch of each for topping the pie. Whip the cream until stiff peaks form.

Mound onto the cooled pie, then top with the remaining zest. Slice and serve.