Since opening in 1944, Strawn's has received tons of attention for its signature icebox pie, and you probably won't get out of the place without trying one. Reminders are everywhere: Cream-topped, fruit-filled pies are painted on the walls and plastered on the front of the menu, and the staff shirts say #PIE. The recipe itself isn't complicated. In the 1920s and '30s, icebox pies were a practical choice for home cooks, who could prebake the shell and then keep the whipped filling cool in an icebox until it was time for dessert. Lemon versions are common in the South, but Strawn's made a name for itself with this fresh strawberry one.
Make the crust: Pulse the flour and salt in a food processor until combined. Add the shortening and pulse until the mixture looks like coarse cornmeal. Add the ice water, then continue to pulse until the mixture becomes a shaggy dough. Form the dough into a disk, wrap in plastic wrap and refrigerate until firm, about 30 minutes.
Roll out the dough on a lightly floured surface into an 11-inch round (about 1/8 inch thick), then fit into a 9-inch pie dish. Trim away any excess dough, crimp the edges and prick the bottom all over with a fork. Refrigerate until firm, about 30 minutes.
Preheat the oven to 350 degrees F. Line the bottom of the pie with foil or parchment paper and fill with pie weights or dried beans. Bake until the bottom is just starting to set and the edges are just starting to brown, 25 to 30 minutes. Remove the foil and weights and continue to bake until the crust is golden brown and cooked through, about 10 more minutes. Transfer to a rack and let cool completely.
Meanwhile, make the glaze: Whisk the eggs with the granulated sugar in a medium bowl until smooth. In a separate bowl, whisk the cornstarch with 2 tablespoons milk until smooth, then whisk into the egg mixture. Warm the remaining 1/2 cup plus 2 tablespoons milk and the melted butter in a medium saucepan over medium-high heat until steaming, 2 minutes. Slowly whisk the warm milk mixture into the egg mixture, whisking constantly, then return the entire mixture to the saucepan. Reduce the heat to medium and cook, whisking constantly, until thickened, about 4 minutes. Whisk in the red food coloring.
Spoon the glaze into the pie crust and spread over the bottom and up the sides. Cover with plastic wrap and refrigerate until set, 2 hours.
Spread the berries in the glazed crust. Dust with confectioners' sugar.
Make the topping: Beat the heavy cream, confectioners' sugar and vanilla in a large bowl with a mixer on medium-high speed until stiff peaks form. Spread over the pie and top with the strawberry half.