In a medium bowl, whisk flour, baking powder and salt together. Set aside.
In a large bowl, beat butter, sugar, dry pudding mix and lemon zest together until combined.
Next, add egg and milk into mixture and beat until creamy.
Gradually add dry ingredients into sugar mixture and beat until combined.
Divide sugar cookie dough in half and roll into a 6 inch roll on a lightly floured surface.
Wrap each roll in plastic wrap and place into the fridge for 4+ hours or overnight.
Preheat oven to 375° and unwrap each roll.
Cut into 1/2 inch slices and place on an ungreased baking sheet.
Bake for 9-10 minutes or until edges just start to brown.
Remove from oven and let sit on baking sheet for a couple minutes then remove to wire rack to cool completely.