In a large bowl, sift flour, salt, and baking powder. Set aside. In the bowl of an electric mixer fitted with the paddle attachment, beat butter and sugar on medium speed until fluffy. Beat in eggs and vanilla. Add flour mixture, and mix on low speed until thoroughly combined. Divide dough in half, wrap in plastic wrap, and roll with rolling pin so plastic is tight and dough is even. Chill until firm, at least 1 hour.
Preheat oven to 325 degrees. Have ready several baking sheets lined with parchment. Remove dough from refrigerator; let stand at room temperature to temper slightly. (This prevents the dough from cracking.) Place parchment on a clean surface; dust generously with flour.
Roll dough to a scant 1/4-inch thickness, stopping often to release the dough by running an offset spatulat under it. Dust with flour as necessary to prevent dough from sticking. Transfer parchment and dough to freezer until very firm, about 15 minutes.
Remove dough from freezer; working quickly, cut into desired shapes. If your dough begins to soften, return to freezer for a few minutes. Using a wide spatula, transfer to baking sheets; freeze or refrigerate until firm, about 15 minutes. Bake 15 to 18 minutes, or until edges just begin to brown, rotating halfway through. Cool on wire racks; decorate.