In a large bowl, combine all-purpose flour and chilled, cubed unsalted butter. Use a pastry cutter or your hands to blend together until the mixture resembles coarse crumbs.

Gradually add ice water, one tablespoon at a time, mixing just until the dough comes together. Form the dough into a ball, wrap it in plastic wrap and refrigerate for at least 30 minutes.

Preheat your oven to 375°F (190°C).

In a separate bowl, combine sliced plums, granulated sugar, cornstarch, ground cinnamon, and freshly squeezed lemon juice. Mix well.

Roll out half of the dough on a lightly floured surface to fit your pie dish. Transfer the dough to the dish and trim the edges. Pour the plum mixture into the crust.

Roll out the remaining dough and cut it into strips to form a lattice pattern over the pie. Brush the lattice and edges of the crust with beaten egg.

Bake for 50-60 minutes, or until the crust is golden brown and the filling is bubbly.

Allow the pie to cool on a wire rack before serving.