Pour the flour and the sugar into a bowl; make a hole in the middle of the mixture, cut the butter into small pieces, then add it, along with the eggs, the Limoncello, the yeast and the Vanilla extract, to the mixture. Knead the dough taking care to thoroughly mix in all the flour.
Keep on kneading until smooth and well blended. Cover the dough with some plastic wrap and let it rest for about half an hour. Once done with previous step, split up the dough into smaller pieces (of about 150g), dust a pasta machine with flour then pass each piece of dough through it to create thin sheets.
Lay down the thin sheets on a pastry board dusted with flour. Fill the lower half of the “bugie” with a layer of hazelnut or strawberry creamed honey. Lightly dampen the top half of the remaining dough sheets with water, then fold it over the other half.
Put pressure on the edge of the “bugie” with your fingers and, in doing so, seal the creamed honey inside of the dough sheet. Stir-fry 2-3 “bugie” at a time, flipping them over a couple of times.
Put the cooked “bugie” onto some blotting paper to get rid of the excess oil. Serve hot, sprinkled with icing sugar.