Combine the milk, water and butter in cup and microwave until the butter is melted and the mixture feels warm, but not hot. If you have a thermometer, it should be between 100°F and 110°F. Pour into stand mixer and mix in the yeast and sugar. Let sit for 5 to 10 minutes until the yeast is bubbly.
The stand mixer should have the dough hook attachment on. Add in your eggs and mix until incorporated. Then mix in your flour and salt until a sticky dough is formed. It should take a few minutes. Once the dough is formed, place it in a large greased bowl and cover with a damp towel. Let it rise in a warm, dry place for an hour or until it has doubled in size.
Liberally flour your work surface. Cut the dough in half and place one half to the side. Roll out the first half until it's about ½ Inch thick. Using a donut cutter, cut out donut rings and place on a baking sheet with parchment paper. Do the same thing with the other half of dough. You should have about 2 dozen donuts. Use the last bit of dough to make a twisted donut if you can't get it in a circle shape.
Let the donuts rise for another 30 minutes. In the meantime turn on your deep fryer and get the oil up to about 350°F-360°F. Make the toppings of your choosing. Get a large plate ready with paper towels on top.
Cut the parchment paper the donuts are on into squares so there is a square of paper under each donut. Depending on how big your fryer is, place 2 to 4 donuts in at a time. Fry on each side for about 2 minutes, until they are a golden brown and then place on the paper towel plate to let excess oil drain off.
Dip the donuts into the icing or glaze of your choosing and top with sprinkles. Store in an airtight container. These are best to eat the day of.