Preheat your oven to 375°F (190°C).
In a mixing bowl, combine flour and salt. Add cold butter and mix until the mixture resembles coarse crumbs. Gradually add ice water and mix until the dough comes together.
Divide the dough in half, shape into discs, wrap in plastic wrap, and refrigerate for at least 30 minutes.
In another bowl, combine mulberries, sugar, cornstarch, lemon juice, and lemon zest. Mix well.
Roll out one disc of dough on a floured surface and fit it into a pie dish. Pour the mulberry mixture into the crust.
Roll out the second disc of dough and place it over the filling. Trim and crimp the edges. Cut a few slits in the top crust to allow steam to escape.
Bake for 45 minutes or until the crust is golden brown and the filling is bubbly. Let cool before serving.