In a medium bowl, whisk together the flour, baking powder, and salt.
In the bowl of an electric mixer, combine the butter and sugar. Beat on medium-high speed until soft and fluffy, ~2 - 3 minutes.
Beat in the eggs one at a time, mixing well after each addition. Scrape down the bowl as needed. Blend in the vanilla.
With the mixer on low, add the dry ingredients. Mix until just incorporated.
Cover dough and chill for 1 hour. Meanwhile, preheat the oven to 350°F and line baking sheets with parchment paper.
When dough is chilled, scoop a scant quarter cup of dough and roll into a ball. I weighed out the whole ball of dough on a kitchen scale and divided it by 24. Each of my cookies was around 2 ounces in weight. Flatten the ball slightly depending on the thickness you desire. The cookies will only spread a bit and not flatten much during baking. Repeat this process with the remaining dough and space the cookies ~2 - 3 inches apart on the baking sheet.
Bake 10 - 12 minutes or just until set. Do not over bake! The edges should not be brown. Remove from oven and let the cookies cool on the baking sheet for several minutes before transferring to a wire rack to cool completely.