Preheat oven to 350°F.
In a medium bowl, stir together flour, baking powder and salt. Set aside. You can weigh the flour on a scale for exact measurement, if desired.
In a large bowl, add the butter and sugar. With an electric mixer, beat on medium for 3 minutes or until light and fluffy. Add the egg and vanilla. Beat on medium for another minute.
Gradually add the flour with the mixer on low. Once it's combined. Turn the mixer up to medium and blend until the dough begins to pull away from the sides of the bowl. Take the dough out of the mixer and place on a piece of parchment paper. Knead the dough with your hands for about a minute. Wrap the dough in the parchment paper and refrigerate for one hour.
Once it's chilled, unwrap the parchment and place on counter (you'll have the dough on the parchment paper). Place another sheet of parchment on top of the dough. Use your body to lean against the counter and hold down the two sheets of parchment on one side. Roll the dough through the parchment paper (so you don't need any extra flour). Roll the dough to about 1/8-inch thick (but slightly thicker, not 1/4-inch though). Using a 3-inch flower cookie cutter, cut them right on the parchment paper, then slide the parchment paper right onto a 13"x18" half sheet pan with raised edges.
Bake the cookies for 8-10 minutes or until just turning golden brown on the edges. Let cool.