Combine pink apples, Granny Smith apples, cranberries, brown sugar, flour, lemon zest, cinnamon, nutmeg, and vanilla together in a bowl and stir until apples are completely coated.
Roll out and line a pie dish with 1/2 the dough. Pour apple mixture into pie dish. Dot apple mixture with butter pieces. Roll out remaining 1/2 the dough and top apple mixture with dough. Pinch edges of bottom and top crusts together. Tuck in dough and crimp to form a border. Cut vents in the top of the dough and place pie on a baking sheet.
Bake pie in the preheated oven until apples are tender, filling is bubbling, and crust is golden brown, about 50 minutes. Transfer to a wire rack to cool.