Step 1: Preheat and Prepare the Donut Pan

1. Preheat your oven to 350°F (175°C).
2. Lightly grease your donut pan or spray with non-stick cooking spray to ensure easy removal after baking.

Step 2: Make the Cinnamon Sugar Swirl

1. In a small bowl, combine the granulated sugar and cinnamon.
2. Add the softened butter and mix it until the cinnamon-sugar mixture becomes a paste. Set aside.

Step 3: Prepare the Donut Batter

1. In a medium-sized bowl, whisk together the flour, sugar, baking powder, cinnamon, and salt.
2. In a separate bowl, mix the milk, egg, vanilla extract, melted butter, and sour cream until well combined.
3. Add the wet ingredients to the dry ingredients and stir until just combined. The batter should be thick and fluffy.

Step 4: Assemble the Donuts

1. Spoon half of the donut batter into the bottom of each donut pan cavity, filling each about halfway.
2. Spoon a small amount of the cinnamon-sugar mixture into the center of each donut and swirl it slightly with a toothpick or knife.
3. Top with the remaining donut batter, ensuring the cinnamon sugar is covered.

Step 5: Bake the Donuts

1. Bake in the preheated oven for 12-15 minutes, or until a toothpick inserted comes out clean and the donuts are lightly golden.
2. Let the donuts cool in the pan for about 5 minutes before transferring them to a cooling rack to cool completely.

Step 6: Prepare the Vanilla Glaze

1. In a small bowl, whisk together the powdered sugar, vanilla extract, and milk until smooth and thick, adding more milk if necessary to achieve the desired consistency.

Step 7: Glaze the Donuts

1. Once the donuts are completely cooled, dip the tops of each donut into the vanilla glaze, allowing any excess glaze to drip off.
2. Let the glaze set for a few minutes before serving.

Step 8: Serve & Enjoy

1. Serve these warm or at room temperature, and enjoy your homemade coffee cake donuts with a cup of coffee or tea!