Preheat oven to 400℉. Line baking sheet with parchment.
Let pie crust come to room temperature 5 - 10 min. Roll pie crust out onto a lightly floured surface. Carefully transfer to lined baking sheet and chill in refrigerator.
In a medium bowl, whisk together zest of 1 lemon and sugar until sugar becomes fragrant and pale yellow. Gently toss 3 cups of strawberry slices into the lemon sugar. Let sit 15 - 20 min, until juices begin to render.
Drain berries, reserving the juice. Whisk 2 tbsp cornstarch into the juice, then gently toss the strawberries back into the thickened juice.
Remove baking sheet with dough from refrigerator. Let sit a few minutes so dough is more pliable. Place strawberry mixture on top of dough, leaving 2" of space around the border. Gently fold the dough over the berries in panels around the circumference.
Brush crust with melted butter. Sprinkle raw sugar around crust. Bake 40 minutes or so, until crust is golden. Rest on cooling rack for 5-10 min.
Slice and serve with vanilla ice cream and a drizzle of aged balsamic vinegar.