Combine the warm water, milk, sugar, and yeast in a large bowl. Whisk to dissolve the yeast. Allow the yeast to proof for about 5 minutes or until it starts to foam.
Add the remaining ingredients. Knead on low using a dough hook on your mixer or by hand. Knead for about 5 minutes or until the dough is nice and smooth.
Place the dough into a greased bowl, cover with plastic wrap and let rise in a warm draft-free place until almost doubled in size, about an hour.
Punch the dough down and roll out on a lightly floured surface to 1/2-inch thick. Use a 3-inch cutter to cut the donuts. Place the donuts on a floured parchment-lined baking sheet, cover with plastic wrap, and let proof for 15 minutes. Re-roll the remaining dough, cut out the remaining donuts and add them to the baking sheet.
Heat 2 inches of oil in a heavy pot (Dutch oven) to 350-360 degrees Fahrenheit. Drop 2-3 donuts at a time and allow to become golden before turning to the other side, about 2 minutes per side.
Remove from the oil and place on paper towel-covered wire rack. Let cool before filling.