In a large mixing bowl, cream together the softened butter and sugar until light and fluffy, about 3-4 minutes.
Beat in the eggs one at a time, then add the vanilla extract and mix well.
In a separate bowl, whisk together the flour, baking powder, and salt.
Gradually mix dry into wet until just combined; do not overmix.
Divide the dough in half, wrap each portion in plastic wrap, and refrigerate for at least 1 hour (or up to 3 days).
Preheat your oven to 350°F and line baking sheets with parchment paper.
On a lightly floured surface, roll out the dough to ¼-inch thickness and cut with cookie cutters. Sprinkle with sugar if desired.
Bake for 8-10 minutes, until the edges are just barely golden. Let cool on the baking sheet for 5 minutes before transferring to a wire rack.