Combine the yeast, water, and milk in your mixing bowl. Let sit for 5 minutes, or until the yeast starts to bloom (foam).
Fit your mixer with the paddle attachment and slowly stir in the sugar, salt, egg, and melted butter.
Add the flour, one cup at a time, and mix until the dough starts to come together and pull away from the side, about 2 minutes.
Mist a glass bowl with cooking spray. Place the dough into the dish, turning once to coat with the spray, and cover with a clean cloth.
Place in a warm area and allow to rise for 1 hour, or until doubled in size.
Turn the dough out onto a lightly floured surface. Roll to 1/2 inch thickness and cut into donut shapes using a cutter.
Place the cut donuts, and donut balls, onto a parchment lined pan. Cover with a clean towel and allow them to rest for 15 minutes.
Heat the oil to 350 degrees.
Fry each donut for 40 seconds on each side, or until golden brown. Remove and place on a cooling rack.