Preheat the oven to 375 degrees F (190 degrees C). Lightly grease a glass, deep-dish pie dish.
Stir together sugar and cinnamon in a small bowl. Whisk milk and eggs together in a separate bowl.
Butter one side of each slice of bread, and cut into cubes. Spread 1/2 of the bread cubes into the prepared pie dish, sprinkle with 1/2 of the cinnamon-sugar mixture, and 1/2 of the shredded apples. Repeat layers once more with remaining bread cubes, cinnamon-sugar mixture, and apples. Pour milk-egg mixture over the top and let sit until bread cubes are moist, about 10 minutes.
Bake in the preheated oven until top is crispy, 40 to 50 minutes. Let cool for at least 20 minutes before serving.