Preheat your oven to 375°F (190°C). Lightly grease your donut pan with butter or non-stick spray.
In a medium bowl, whisk together the all-purpose flour, granulated sugar, baking powder, salt, and 1 tablespoon ground cinnamon.
In a separate large bowl, whisk the melted butter, milk, eggs, and vanilla extract until well combined and smooth.
Slowly add the dry ingredients to the wet ingredients, stirring gently until just combined. Do not overmix; a few lumps are okay.
Spoon the batter into the prepared donut pan, filling each cavity about 3/4 full.
Bake in the preheated oven for 12-15 minutes, or until a toothpick inserted into the center comes out clean and donuts are slightly golden on top.
While the donuts bake, mix 1 cup granulated sugar with 1 tablespoon ground cinnamon in a small bowl. Once donuts are warm but cool enough to handle, brush or spray them with melted butter, then roll each donut in the cinnamon sugar mixture until evenly coated.
Serve fresh or store as desired.