Preheat oven to 400 degrees F (200 degrees C). Grease an 8-inch pie plate.
Mix zucchini, carrots, and butternut squash together in a large bowl. Sprinkle cornstarch, salt, and pepper over the vegetable mixture and toss to coat.
Line pie plate with one of the pie pastries, trimming edges to fit the plate. Pour vegetable mixture over the pie pastry. Drizzle most of the melted butter over the vegetables. Place remaining pastry atop the vegetables. Press edges of the two pastries together to seal. Brush top of the "cobbler" with remaining butter. Cut several slits in the top pastry.
Bake in preheated oven until top is golden brown, about 30 minutes. Rest pie for 10 minutes before cutting to serve.