Remove pie crusts from the refrigerator and let stand at room temperature while filling is prepared.
Heat 2 tablespoons butter in a large skillet until melted. Add apples, 1/8 teaspoon salt, 1 1/4 teaspoon cinnamon, white sugar, and 3 tablespoons of water. Stir until well combined and bring mixture to a simmer. Cook, stirring occasionally, until apples are tender, about 8 to 10 minutes.
Meanwhile, whisk together remaining water and cornstarch until it is dissolved. Add cornstarch mixture to apple mixture and stir until well incorporated. Bring mixture to a simmer and cook one minute until thickened. Remove from heat and let cool.
Meanwhile add flour and brown sugar to a bowl. Add in remaining butter, salt, and cinnamon and mix with hands or a fork until well combined and crumbly. Set aside.
Preheat the oven to 400 degrees F (200 degrees C). Stack 2 pie crusts on top of each other and press them together. Use a rolling pin to roll the crust out to 12 to 14 inches and to form one crust. Transfer dough to a pizza pan and, If desired, crimp the edges like a pie.
Sprinkle crust with cheese and top with apple mixture. Add brown sugar crumble evenly to the top.
Bake in the preheated oven until browned and bubbly, 22 to 25 minutes. Let stand at least 10 minutes before serving.
Whisk confectioner’s sugar and milk together and drizzle mixture over the “pizza.” Cut into wedges and serve.
