1. Preheat your oven to 350°F (175°C) and grease a donut pan or line a baking sheet with parchment paper.
2. In a large mixing bowl, whisk together the flour, sugar, baking powder, and salt.
3. In a separate bowl, combine the eggs, vanilla extract, melted butter, milk, and cooled brewed coffee. Mix well.
4. Gradually add the wet ingredients to the dry ingredients, stirring until just combined. Do not overmix.
5. Pour the batter into a piping bag or zip-top bag with the tip cut off, then fill each donut cavity about ¾ full.
6. Bake for 12-15 minutes or until a toothpick inserted into the donuts comes out clean.

Making the Coffee Glaze

1. In a small bowl, whisk together the powdered sugar and brewed coffee until smooth.
2. Adjust the consistency by adding more coffee or powdered sugar as needed.
3. Once the donuts are cooled, dip the tops into the glaze and let set. Add toppings like sprinkles or cinnamon sugar for extra flavor.