1. Prepare Your Donut Pan and Oven: Begin by preheating your oven to 350 F (175 C). Lightly grease a mini donut pan with cooking spray or butter. This step is crucial for easy release of your baked donuts.

2. Combine Wet Ingredients: In a large mixing bowl, whisk together the sourdough discard, granulated sugar, egg, milk, melted and cooled butter, and vanilla extract until the mixture is smooth and well combined. Ensure there are no lumps of sugar or egg.

3. Whisk Dry Ingredients: In a separate medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Make sure these dry ingredients are thoroughly combined to ensure even leavening throughout the donuts.

4. Combine Wet and Dry Mixtures: Gradually add the dry ingredient mixture to the wet ingredients, mixing only until just combined. Be careful not to overmix the batter; a few small lumps are perfectly fine. Overmixing can lead to tough donuts.

5. Fill the Donut Pan: Transfer the donut batter into a piping bag or a large Ziploc bag with the corner snipped off. Alternatively, you can use a spoon, but a piping bag makes filling the donut cavities much neater and easier. Fill each donut cavity about two-thirds full. This allows room for the donuts to rise without overflowing.

6. Bake to Golden Perfection: Place the filled donut pan in the preheated oven and bake for 10-12 minutes, or until the donuts are golden brown and spring back when lightly touched. A toothpick inserted into the center should come out clean.

7. Cool and Glaze: Remove the donut pan from the oven and let the donuts cool in the pan for 5 minutes before carefully transferring them to a wire rack to cool completely. While they cool, prepare the glaze by whisking together the powdered sugar, milk, and vanilla extract until smooth. Dip the cooled donuts into the glaze, letting any excess drip off, then place them back on the wire rack for the glaze to set.