In a large bowl, whisk together flour and salt.
Add cold butter and shortening, and cut into the flour mixture using a pastry blender or your fingertips until it resembles coarse crumbs.
Add ice water, one tablespoon at a time, mixing until the dough just comes together.
Divide dough in half, shape into discs, and chill for at least 1 hour.
On a lightly floured surface, roll out one disc to fit a 9-inch pie dish. Press into the bottom and up the sides.
Place sliced strawberries in a bowl, add 1/4 cup sugar, cornstarch, and lemon juice. Toss to coat and let sit for about 10 minutes.
Pour strawberry mixture into the pie crust and dot with tablespoons of water to help steam the filling as it cooks.
Roll out the second disc of dough for the top crust. Cover the pie filling and crimp the edges to seal. Cut slits in the top for steam to escape.
Chill the pie in the refrigerator for at least 1 hour before baking.
Preheat oven to 375°F (190°C). Bake the pie for 50 minutes, or until the crust is golden and the filling is bubbly.
While the pie is baking, mix 1 tablespoon of cold water with the remaining 1 tablespoon of sugar, then brush this glaze over the top of the pie once it’s out of the oven and slightly cooled.
Cool completely before serving.