Preheat oven to 350 degrees F (175 degrees C). Butter an 8x8-inch baking dish.
Mix doughnuts and apple together in the prepared baking dish.
Whisk half-and-half, sugar, eggs, vanilla, and cinnamon together in a bowl. Pour half-and-half mixture over donuts and apples in the baking dish. Let sit until liquid is absorbed, stirring occasionally, about 15 minutes.
Bake in the preheated oven until golden, about 30 minutes. Cool and drizzle with maple syrup.