In the bowl of a stand mixer, fitted with paddle attachment beat butter for 3 minutes until creamy. Add sugar and vanilla and beat until incorporated. Add egg and mix until combined.
In a large bowl sift flour and add baking powder and salt. Gradually add flour to wet ingredients. Mix until flour is incorporated.
Form a ball from the dough, wrap in plastic wrap and refrigerate for 2 hours or overnight.
Take out of the fridge, when ready to make the cookies. Separate dough in half, make 2 balls. Roll each half between parchment paper, until dough is 1/4n inch thick. Using an egg shaped cookie cutter, cut out cookies. Try to cut as many as you can. You can of course re roll the dough, but every time you do, tiny air pockets may form and cookies will not be as smooth.
Preheat oven to 350 F. Transfer cookies to a baking sheet lined with silpat or parchment paper. Bake cookies for 10-11 minutes, until they are barely beginning to turn golden. Let cookies cool on baking sheet for 10 minutes, then transfer to a cooling rack to cool completely.