In a medium bowl, whisk together the flour, sugar and salt. Cut in the shortening and butter until the mixture resembles small peas.
In a separate bowl, mix egg, 7 tablespoons water and vinegar. Add to the dry ingredients and stir with a fork just until combined. Add another tablespoon of water if the mixture is still dry.
Spoon out onto parchment or waxed paper and use your hands to mold together. Divide into two equal parts and shape each into a disk. Wrap with plastic wrap and refrigerate for at least 30 minutes (you can freeze the 2nd piece, if you'd like- since you'll only need one for this recipe).
Preheat the oven to 350 degrees F.
Roll the dough out on a lightly floured surface to 16 inch diameter round. Transfer to 9-inch diameter glass pie dish (not deep dish). Trim edges and crimp decoratively. Pierce crust all over with a fork. Bake until crust is golden- about 35 minutes. Let cool.
FILLING
Place sliced strawberries in the cooled crust.
In the top of a double boiler (see tips below if you do not have a double boiler), whisk together egg yolks, sugar, lime juice, tequila and zest. Set over simmering water and whisk constantly until the custard thickens and registers 170 degrees F. on a candy thermometer (should take 4 to 5 minutes). Be sure to continue mixing the entire time. If you leave the yolk mixture to warm by itself, it's going to want to begin turning into scrambled eggs!
Remove the upper pan from the water and whisk in the butter. Cool slightly, then pour the filling on top of the strawberries. Refrigerate until the filling sets (3 hours or overnight).
TOPPING
Mix whipping cream and sugar with a mixer until thickened. Spread over the top of the pie.
Refrigerate until ready to serve. Garnish with strawberries, if desired.
Notes
If you do not have a double-boiler, set a metal mixing bowl over a pot of simmering water. Mix in the mixing bowl, and it will work just the same.