Begin by bringing the butter to room temp by leaving it out on the counter for 20 minutes or so.
Mix the softened butter with the sugar until light and fluffy.
Add the flour, baking powder, and salt.
Mix well, and then bring together into a ball with your hands, the mixture will be crumbly until you do so. You'll have to "press it" into a ball. The key to successful shortbread cookie dough is to handle it as little as possible. Don’t pound or knead it heavily or this can affect the levity of the shortbread.
Form a disk with the dough, wrap in plastic and refrigerate for 30 minutes.
Roll out into 1/4 inch thickness.
Using a sharp knife or pizza cutter, cut into rectangles. You can also use a cookie cutter, if that's easier for you.
Poke a fork carefully into the little rectangles, creating holes. This helps with even cooking. Place in the refrigerator for thirty minutes.
Bake on an ungreased cookie sheet for 20 minutes at 350°.
Remove to the cooling rack, and serve.