Prepare the apples: Peel and finely dice the apples into small pieces so they distribute evenly throughout the donuts.
Cook the apple mixture: Melt the butter in a small skillet over medium heat. Add the diced apples, brown sugar, and cinnamon. Cook for about 3–5 minutes, stirring occasionally, until the apples are slightly tender but not mushy. Remove from the heat and let cool.
Prepare the oven and pan: Preheat the oven to 350°F (175°C). Lightly grease a 12-cavity donut pan with cooking spray or butter.
Mix the dry ingredients: In a large bowl, whisk together the flour, granulated sugar, baking powder, baking soda, cinnamon, and salt.
Mix the wet ingredients: In a separate bowl, whisk together the egg, milk, melted butter, and vanilla extract until smooth.
Make the batter: Pour the wet ingredients into the dry ingredients. Gently stir with a rubber spatula until just combined. Do not overmix, as this can make the donuts dense.
Add the apples: Gently fold the cooled apple mixture into the batter until evenly distributed.
Fill the donut pan: Spoon or pipe the batter into the prepared donut cavities, filling each about two-thirds full. Avoid filling them all the way to the top.
Bake: Bake for approximately 13–16 minutes, or until the donuts are lightly golden and a toothpick inserted into the thickest part comes out clean.
Cool: Let the donuts cool in the pan for about 5 minutes, then carefully transfer them to a wire cooling rack.
Prepare the coating: In a small bowl, combine the granulated sugar and cinnamon.
Coat the donuts: While the donuts are still slightly warm, lightly brush each donut with melted butter, then gently toss or sprinkle with the cinnamon-sugar mixture.
Serve: Serve the Apple Cinnamon Donuts warm or at room temperature with coffee, tea, apple cider, or your favorite breakfast beverage.