In a large mixing bowl (or in the bowl of the standing mixer), whisk together the softened butter, sugar, liqueur, lemon zest and vanilla extract until smooth. Add the eggs and whisk again.
Then incorporate the baking soda, along with the flour by cupfuls until you've formed a smooth, soft but non-sticky dough. )I usually begin with a whisk, then switch to a wooden spoon or spatula when the dough gets too solid to whisk, then once I have a ball, switch to hand kneading.)
Let the dough rest for 30 minutes or so.
Take perhaps 1/4 of the dough and roll it out on a lightly floured pastry/cutting board with the palms of your hands into a log about 2cm (3/4 inch) thick, as if you were making potato gnocchi. Cut the log into 2 cm (3/4 inch) sections, then take each section and roll it in the palms of your hands into round balls. Place the balls onto a lightly floured baking sheet.
Deep fry the balls in moderately hot (180F/350C) oil until golden brown on all sides, about 2-3 minutes. Using a spider skimmer, toss the dough balls gingerly in the oil now and again so they brown evenly on all sides. The should puff up considerably. Drain on paper towels or a baking rack.
While still warm, sprinkle your fried castagnole with sugar and toss until well covered on all sides.
Serve at room temperature.