In the bowl of a stand mixer, combine 4 cups of the flour, sugar, salt and yeast. Mix to combine. Grate the cold butter into the flour mixture and toss to coat the butter with flour.
Make a well in the center of the flour mixture and add in two eggs, milk, water and vanilla. The water and milk should be at least 120º F to activate the yeast.
Using the hook of the stand mixer, or a wooden spoon if mixing by hand, mix the ingredients until a soft, slightly sticky dough is formed. Add more flour, 1 tablespoon at a time if needed.
Knead for about 5 minutes.
Place the dough in a lightly greased bowl, cover and allow to rise in a warm place for at least an hour, until it has doubled in size.
Punch down the dough and place on a lightly floured surface, roll out to about 3/4 inch thick.
Cut the donuts into 3 inch rounds with a 1 inch circle in the center
Place the donuts onto a parchment lined baking sheet, cover and let rise for 30 minutes.
Heat about 3 cups of oil in a deep dutch oven pan or pot to 325º F. Carefully fry the donuts for about 3 minutes per side until they are golden brown.
Place onto a cooling rack over a paper towel lined baking sheet.
While the donuts are still warm, dip the top into a chocolate glaze or the whole donut into the vanilla glaze.
In a large mixing bowl, whisk together the powdered sugar, milk and vanilla until the glaze has formed. Dip warm donuts into the glaze, then place onto a cooling rack to allow excess to drip off of the donuts.
Microwave the heavy cream for 30 seconds to 1 minute, until very hot. Add in the chocolate chips and vanilla and stir until the chocolate chips are melted. Dip the tops of the warm donuts into the chocolate, shake off any excess as needed.
Nutrition facts are just an estimate.
Use a thermometer to monitor the temperature of the cooking oil. The temperature of the oil will go down as donuts are added to the oil, just adjust the heat as needed.
For ease of cooking, use a chopstick to place the donuts into the oil as well as to flip the donuts.