In a medium bowl, sift together the flour, salt, and baking powder. In a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, beat the butter and sugar together on medium speed until light and fluffy, about 2 minutes. Add the eggs, one at a time, while mixing. Scrape down the sides of the bowl. Beat in the vanilla. With the mixer running, gradually add in the flour mixture and mix until everything is well incorporated. Divide the dough in half, shape into two disks, and tightly wrap in plastic wrap. Refrigerate for 2 hours or up to 2 days. (if chilling longer than 2 hours, let the dough sit at room temperature for 15 to 30 minutes or until slightly softened.) Once the dough is chilled and you’re ready to bake, preheat the oven to 375F. Roll the dough on a lightly floured surface to ¼-inch-thickness. Cut out shapes using 2½-inch cookie cutters. Re-roll as needed for more cookies. Place the cut-outs on non-stick or parchment-lined baking sheets 1 inch apart. Bake one sheet at a time for 10 to 12 minutes or until the bottom edges start to turn brown. Let cool for a few minutes on the pan then transfer to a wire rack and cool completely. Serve plain or decorate with royal icing.