In the stand mixer add the warmed milk and yeast let it sit for 5 minutes. Add the eggs, melted butter, and sugar. Using the flat beater attachment, mix all until combined.
Add the dough hook now and add 4 1/2 cups of flour. Mix on medium speed until the dough starts to pull away from the bowl. If the dough is too sticky add 1-2 tablespoons of the remaining flour at a time. You may not use the whole ½ cup. Top the bowl with plastic wrap and let the dough rest for 1 hour or until doubled in size.
Roll out the dough to about ½ inch thick and using a 1.5-inch biscuit cutter cut out your donuts. Lightly roll the donuts in the palm of your hand to form a ball. Put the donuts on a baking sheet lined with greased parchment paper.
Then, top the donuts with a piece of plastic wrap sprayed with cooking spray to prevent the donuts from drying out. Allow the donuts to rise for 30 minutes.
Use a deep pot or dutch oven filled with 2 inches of oil (about 4 cups). Preheat the oil to 350 degrees. Working in batches, fry the donuts for 2-3 minutes.
Put the cooked donuts on a cooling rack lined with paper towels for up to 1 minute. Then toss them in the cinnamon sugar and completely coat.
Once the donuts have completely cooled place a donut on a lollypop stick and place it in a mug filled with rice. Continue until you have made enough to fill the mug. Enjoy!