In a small bowl, add the flour, baking powder, lemon zest and whisk together; set aside.
In a large mixing bowl add the butter, sugar, and vanilla; mix together with a wooden. Stir in the milk. Add in the flour and mix all the ingredients together (including the lightly beaten eggs).
Dump the dough onto a lightly floured and clean surface and gently knead until combined, adding a spoonful of flour if needed if you find the dough is too sticky. When the dough is smooth, roll out portions a bit at a time into 1-inch thick logs and cut into 1-inch pieces. Cover the remaining dough with a clean tea towel until you are ready to work with it.
Add the oil into your pan on medium high heat. When the oil is hot enough (temperature should be 350F), start adding about 8 dough balls at a time. Turn them around while frying so that all sides get color and that they aren’t raw in the middle. Remove the castagnole with a slotted spoon and place them on a paper towel lined plate.
When completely cool, dust with confectioner’s sugar.