Combine warm milk, yeast, and sugar together and let the yeast bloom.  This will take about 5 minutes for the yeast to start to bubble and foam up.

In a stand mixer, fitted with a dough hook mix together eggs, sugar, salt, and melted butter until it is combined.  

Add in yeast mixture and mix until the yeast is incorporated.  

Add in flour and mix until everything is combined and the dough is starting to pull aways from the sides.  

Turn the dough onto a lightly floured surface and knead for about a minute, just until the dough is nice and smooth.  

Place in an oiled bowl, cover with a towel, and let rise until doubled in size.  About 1 hour.  

After the dough has risen, place it on a lightly floured surface and roll to about 1/2 inch thick.  Cut the donuts out with a donut cutter, a cookie cutter or even a drinking glass. Gently knead the scraps of dough together and re-roll. If the dough springs back and doesn't roll out, let it rest for 5 minutes and then continue.

Place the donuts on a lined baking sheet, cover and let rise for about 45 minutes.  

Meanwhile heat oil in a large heavy bottom pan.  Heat to 375 degrees.  Set up a cooling rack over a baking sheet so the donuts can drain as they cool.

Carefully add the donuts to the oil, only do a few at a time, and cook for 3-4 minutes, flipping half way, until they are a deep golden color.  Remove from the oil and place on the baking rack to cool.  

Once the donuts are cool top with icing.

Mx together all of the ingredients until smooth. If the mixture is too thick add milk (1/2 teaspoon at a time) until you get the desired consistency.

Using the microwave, melt chocolate chips, butter, corn syrup and milk together in 30 second increments, stirring after each tie. Once it is completely melted and smooth you can dip the donuts.

Once the donuts have cooled dip the donut into the icing and gently twist to coat. Remove and place on the wire rack. If using sprinkles add immediately before the icing sets.