My mother and aunts grew up in the east end of Glens Falls NY. They had a great friend, Helen P., who was also Italian. They shared many years of friendship, cups of coffee and recipes. This is her recipe for Italian cookies (a little more lemony than Grandma's)
Beat the eggs, add sugar, cooled melted butter, oil, lemon and milk. Mix well. Add baking powder to 2 cups of flour. Then add the liquid to the dry ingredients. Knead to make a soft dough. (you may have to add a smidge more flour) Take some of the dough and form a long rope, form into knot shapes or snails. You can also just make balls. Bake at 375 for 10 minutes, check the bottom, they should be golden (but the tops stay pretty pale). Cool and glaze with Confect. sugar mixed with hot water and top with candy sprinkles or colored sugars. Wipe the bottoms clean of any glaze. This recipe can be doubled.