In a large bowl, combine the flour, sugar, vanilla sugar, baking powder, salt, and lemon zest.
Mix in the eggs, butter, and grappa to form a dough.
Knead on a lightly floured surface until smooth. Cover with plastic and allow to rest at room temperature for 1 hour.
Divide the dough into four equal pieces.
Place one piece on floured work surface and cover the rest.
Roll the dough into a rectangle as thinly as possible, flouring as needed to prevent sticking.
Use a fluted pastry wheel to cut and detail the edges of the rectangle.
Cut the dough into 2 x 4 inch (5 x 10 centimeter) strips. If desired, cut 1-2 lines inside each strip.
Place on a large baking sheet lined with parchment and cover while you repeat with remaining pieces.
Add about 3 inches (7.5 centimeters) of oil to a large, deep pan. Place over medium heat to get the oil to 350˚F (180˚C).
Once heated, add a few chiacchiere, being careful not to overcrowd. Fry until lightly golden, about 45 seconds, then turn to fry the other side. Adjust the heat as needed between medium and medium low.
Place on towel lined plates. Repeat with remaining chiacchiere. Serve with powdered sugar.