Preheat oven to 400 Degrees and line a baking sheet with parchment paper or a silicone mat.
In a large saucepan, add milk, water, sugar, and salt and stir over medium heat. Add the butter and allow to melt. Once the butter has melted, bring the mixture to a rolling boil. Stir in the flour, vanilla extract, and stir vigorously with a wooden spoon until mixture forms into a ball that leaves the sides of the pan. Stir hard with wooden spoon for 1-2 minutes before removing from burning. Finally, turn to a mixing bowl and allow to cool for 5 minutes.
Using a standing or hand held mixer, beat in the eggs one at a time until mixture is smooth and glossy. Spoon the mixture into a pastry bag fitted with a ½ inch star tip. On the prepared baking sheet, pipe the batter into 4 inch circles with another circle on the top making concentric circles. If you don’t have a pastry bag use a spoon to make circles as best you can.
Bake the pastry for 15 minutes on 400 Degrees and reduce oven temperature to 375 Degrees and bake for another 15-20 minutes or until doughnuts are light in texture and medium brown all over. Allow to cool slightly.
To make the glaze: whisk all ingredients together ( butter, powdered sugar, water, and vanilla extract) until a thick glaze consistency forms. Dip the tops of the doughnuts in the glaze and turn to a cooling rack and allow glaze to set.
