In a large bowl, cream together butter and sugar until light and fluffy. Mix in vanilla, then add the egg and mix in until just incorporated. Don't over mix.
Gradually mix in flour, 1 cup at a time. Add the baking powder and salt to 1 of the cups of flour before mixing in. Beat until fully incorporated.
Turn dough out onto a floured surface and form into a disc. If making immediately, roll out to about 1/4-1/3 inch thick. If not making immediately, wrap in plastic wrap and store in the fridge or freezer.
Bake cookies at 330 degrees for 15 minutes, or until just barely golden around the edges.