Warm up the milk, then mix in the sugar and yeast. Allow the yeast to sit for about 10 minutes in a dark, warm place until it rises and the top becomes puffy.
In a large bowl, mix the flour, sugar, olive oil, lukewarm water, and the risen milk/yeast mixture together. Whisk it for a few minutes until a smooth batter is formed.
Put the dough in the bowl. Cover the bowl with a dish towel, and put in a dark, warm environment for about an hour, or until the dough rises and doubles in size.
Fry the batter in the oil, a few donuts at the time. When one side turns golden brown, flip them over so that they are evenly browned on each side.
Use a slotted spoon to remove them from the oil and place them on a plate lined with paper towels. Pour the honey over the donuts. Then sprinkle the donuts with chopped walnuts and cinnamon.
If you are storing leftover loukoumades, make sure to allow them to cool all the way before putting plastic wrap on them. Do not add honey to the donuts that you want to save them for another day.