Mix flour, salt, baking powder, and vanilla pudding together and set aside.
In a stand mixer, beat butter until fluffy. Add sugar, eggs, and vanilla. Add dry ingredients and milk. Mix well. Chill for two hours.
Dough can be rolled out and cut with a cookie cutter. Or you can roll the dough in balls and then roll in sugar.
Bake at 375* for 8 to 9 minutes. Let cool on baking sheet until almost cooled. Transfer to a wire rack to finish cooling. Finished cookies can be frosted if desired.