Preheat your oven to 375°F (190°C).
In a mixing bowl, combine flour and salt. Cut in the cold butter until the mixture resembles coarse crumbs. Gradually add ice water, mixing until dough forms. Divide dough in half, shape into disks, wrap in plastic, and refrigerate for at least 30 minutes.
Roll out one disk of dough on a floured surface and fit it into a pie dish. Trim excess dough.
In a large bowl, combine mulberries, sugar, cornstarch, lemon juice, and vanilla extract. Pour filling into the pie crust.
Roll out the second disk of dough and place it over the filling. Trim, seal, 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.