Put the flour, sugar, vanilla sugar, lemon zest, yeast, vanilla essence and the egg in a big bowl and mix together, either by hand or with a kitchen mixer with a dough hook.
When all the ingredients are incorporated, start adding the milk, bit by bit.
Then, start adding the oil bit by bit.
Knead the dough for 10 minutes with the mixer, and 20 by hand.
Move the dough in a bowl brushed with oil, cover it with a tea towel, and leave for an hour in a warm place to rest.
Meanwhile, make the syrup.
Put the water with the sugar in a small pot, over a low heat.
When the sugar dissolves in the water, add the vanilla essence and wait until the mixture starts boiling.
Turn the heat off and add the lemon or orange peel.
Set aside, keeping it warm.
Take a piece of the dough, round it in your hand, and start rolling it between your hands, until you reach a long, thin, strand.
Start rolling it from one side towards the middle, as it was a snail shell. Once you read the middle, do the same from the other side, in the opposite direction.
Do the same for all of them. You should get 6-7 mucenici from this quantity of ingredients.
Cover a tray with baking paper and place the mucenici on it, not too close to each other as they will rise in the oven.
Let them rest for another half an hour.
Preheat the oven at 180 degrees Celsius.
Brush the mucenici with an egg, and then put the tray in the oven and bake for 20-25 minutes, until they are golden brown. You can check if they are done by pricking them with a toothpick. If it comes out clean, they are done.
Let the mucenici cool down, before you put the syrup over.
Then, glaze them with honey and sprinkle chopped walnuts on top.