Use a mixing bowl add in warm milk and water and dry yeast, mix it thoroughly . Let sit for 5 minutes. If the yeast bubbles,it is ready to go, if this is not the case add in more yeast
Using a large bowl mix in the butter, egg yolks, sugar, salt, and cinnamon to liquid. Then add in flour in 3 batches. Start mixing it with a spoon until dough forms a tight ball. If the dough is sticking to the side of the bowl, add more flour by the tablespoon. After mixing it start kneading it on a lightly floured surface for a few minutes until the dough is soft, but not sticky.
After prepping the dough put it in a lightly oiled large bowl. Cover and let rise for 2 hours at room temperature. It should at least double in size.
When dough has risen, turn out onto lightly floured surface and roll out dough until it's 1/4 inch thick. Use circular cutters to cut out donut shapes. If you have a tiny cutter, you can cut out the holes for the donuts, but you can also just leave them whole.
Meanwhile, pour neutral oil in a heavy pan (cast iron or dutch oven) until the oil comes about 1.5-2 inches up the pan. That's all you need to fry these since the donuts float. Heat the oil until it reaches 350°F. Use a candy/deep-fry thermometer to ensure safe temperatures.
Once oil is hot, add donuts and cook for 60-90 seconds on each side until lightly browned. You will probably have to work in batches.
Remove donuts once they are done on each side and let cool on drying rack.
For glaze, melt butter in a bowl and whisk in corn syrup and milk until it's well dissolved. Add vanilla extract. Sift in powdered sugar until glaze is thick but still liquid.
If you're coloring your glazes, add a few drops of food coloring until you get the desired colors. NOTE: If you let the glaze sit for a few minutes, it will start to harden (that's what glazes do). To bring it back to life, just stir in a few drops of warm water.