Preheat oven to 350F. Lightly grease a 12-cavity donut pan with nonstick spray or butter, making sure to coat the center posts well so donuts release cleanly.

In a large bowl, whisk together the flour, sugar, baking powder, cinnamon, and salt until no lumps remain.

In a separate bowl, whisk the milk, melted butter, egg, and vanilla until combined. Pour into the dry ingredients and stir with a rubber spatula just until no streaks of flour remain - do not overmix or donuts will be tough.

Transfer batter to a large piping bag or zip-top bag with a corner snipped off. Pipe batter into each donut cavity, filling about two-thirds full. Smooth tops with a damp finger if needed.

Bake for 10-12 minutes until donuts spring back when lightly pressed and are golden at the edges. Let cool in the pan for 5 minutes, then turn out onto a wire rack.

While donuts are still warm, stir together the sugar and cinnamon in a shallow bowl. Brush each donut all over with melted butter, then toss in the cinnamon-sugar until evenly coated. Return to the wire rack to set.