Prepare the Dry Ingredients: Preheat the oven to 350°F. Lightly grease a donut pan. In a large bowl, whisk together the flour, granulated sugar, baking powder, cinnamon, and salt until evenly combined.
Mix the Wet Ingredients: In a separate bowl, whisk together the milk, egg, melted butter, and vanilla extract until smooth and well combined.
Make the Donut Batter: Pour the wet ingredients into the dry ingredients. Gently stir with a spatula just until the batter comes together. Avoid overmixing, as this can make the donuts dense.
Fill the Donut Pan: Transfer the batter to a piping bag or carefully spoon it into the prepared donut pan. Fill each cavity about three-quarters full, leaving enough room for the donuts to rise.
Bake the Donuts: Bake for about 10–12 minutes, or until the donuts are lightly golden and spring back when gently pressed. Avoid overbaking to keep the centers soft and tender.
Cool Slightly: Let the donuts cool in the pan for about 3–5 minutes, then carefully transfer them to a wire rack. Keep them slightly warm for the best cinnamon sugar coating.
Brush With Butter: Brush each warm donut lightly with melted butter, making sure the butter reaches the surface evenly.
Coat With Cinnamon Sugar: Combine the granulated sugar and cinnamon in a shallow bowl. Immediately roll each buttered donut in the cinnamon sugar mixture until generously coated on all sides.
Serve Warm: Arrange the cinnamon sugar donuts on a serving plate and enjoy them warm with coffee, tea, hot chocolate, or a cold glass of milk.