Cream the soft butter with the sugar until the combination is smooth, not grainy to the touch in a mixing bowl.
Add the eggs and vanilla extract. Mix until combined.
Sift the flour, baking powder, and salt together. Add the dry mixture to the wet mixture. Continue mixing to make sure all ingredients are thoroughly blended.
Make the dough into a ball, wrap it in cling wrap completely covering the entire dough ball.
Put in the refrigerator for about 6 hours or overnight.
Check to see if the dough is firm. Pull the cookie dough out of the refrigerator and sit it out to soften up a bit.
Preheat the oven to 350 degrees Fahrenheit.
Put flour out on the wood cutting board, rub flour on the rolling pin, and work some flour into the batter (if needed). Use a shamrock shaped cookie cutter begin to make your cookies.
Line a baking sheet with parchment paper.
Using a metal spatula move the cut cookies to the parchment lined cookie sheet.
Bake for 8-10 minutes until the cookies are lightly browned around the edges.
Let the cookies sit on the baking sheet for 5 minutes before moving the cookies to a wire rack to cool completely.