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 add the dry ingredients to the wet ingredients, mixing just until combined. Don't 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.