Preheat oven to 350 degrees F (175 degrees C). Line a 9-inch pie dish with the pie crust, and place the pie dish onto a baking sheet.
Place zucchini into the work bowl of a food processor, and process until pureed. Transfer the puree to a bowl, and whisk with eggs, 1 cup white sugar, 1/2 cup melted butter, 2 tablespoons flour, and the vanilla extract. Pour the mixture into the pie crust.
Place 1/2 cup flour, brown sugar, and 3 tablespoons of butter into a bowl, and cut the mixture with a pastry cutter until the topping resembles coarse crumbs. Sprinkle the topping evenly over the pie filing.
Bake in the preheated oven until the filling is set and the topping is lightly browned, about 45 minutes. Allow to cool for at least 30 minutes before serving.