In the bowl of a stand mixer, with the dough attachment, add 1 cup lukewarm water and 2 1/2 tbsp of active dry yeast. Whisk together and let stand for 5 minutes to allow the yeast to activate.
While waiting, measure out flour, sugar and salt into a separate bowl and mix to incorporate sugar and salt into flour.
Once the yeast has had time to activate, add the lukewarm milk, turn the mixer on to a slow speed 2 to start and slowly begin to add the flour, sugar, salt mixture into the bowl of the stand mixer. Add the extra virgin olive oil and move the speed up to a medium or 4 and continue to mix until you achieve a smooth batter.
Cover the mixing bowl tightly with plastic wrap and set aside in a warm place for an hour to rest and rise.
While waiting for the dough to rest and rise, prepare the syrup and chocolate sauce for the Loukoumades. Combine the sugar, water, honey and cinnamon stick into a saucepan and bring to a boil while slowly stirring. Reduce the heat and continue to cook for 3-5 minutes while stirring to ensure the sugar and honey have dissolved. Remove from heat and set aside to cool.
For the chocolate sauce, simply melt the milk chocolate or semi sweet chocolate chips in a double boiler over medium heat. Be sure to stir to prevent chocolate from burning. Once melted, cover and set aside to keep warm.
Prepare a pot to fry the loukoumades by adding 2-3 inches vegetable oil and bringing oil to a temperature of 350° F. Have a glass of water near the bowl with the dough so that you can dip the spoon into the water before each dip into the batter so that the dough doesn't stick to the spoon. Please note, that I use a tablespoon to make nicely sized lukoumades. Once the dough for the loukoumades is ready, give it a stir with a plastic spatula before you begin the process.
Begin to add a tablespoon full of dough into the hot vegetable oil, dip the spoon in water and then repeat until you have enough loukoumades to comfortably fill the pan and so that you are still able to move them around with a meshed strainer or slotted spoon. (I prefer the meshed strainer.) Stir to turn the loukoumades so that they cook as evenly as possible and don't burn.
Remove cooked loukoumades from the oil and place onto a paper towel covered dish to drain. Repeat process until you have used all the dough.
For half the loukoumades, dunk several at a time into the syrup mixture and stir with a large spoon to cover the loukoumades with the syrup. Remove from the syrup and put on a serving dish. Sprinkle crushed walnuts on top.
Plate half the loukoumades onto another serving dish and pour the chocolate sauce on top. Leave plain or sprinkle crushed walnuts on top.