Cream the softened butter with the sugar until smooth.
Add in the eggs, one at a time. Mix until smooth.
Add in the vanilla. Continue mixing.
Sift the flour, baking powder, and salt together in a separate bowl.
Add the dry mixture to the wet mixture.
Continue mixing to make sure all ingredients are thoroughly blended.
Form the dough into a ball. Wrap it in cling wrap.
Put it in the refrigerator for about 6 hours or overnight. Make sure the dough is firm to the touch.
Preheat oven to 325 degrees.
Take the cookie dough out of the fridge and set it aside to soften up a little bit. (While the oven is preheating).
Put some flour out on the cutting board, rub flour on the rolling pin, and (if needed) work some flour into the batter.
Roll the dough out on the cutting board, use the cookie cutter to cut out your cookies.
Line the cookie sheet with parchment paper.
Use a metal spatula to move the cut cookies to the parchment lined cookie sheet.
Bake at 325 degrees for 8 minutes. Check to see if the cookies are thoroughly baked.
Take the cookies off of the cookie sheet and allow to cool on a wire rack for approximately 10 minutes.