Mix the baking powder, salt, and flour in a small bowl and set aside.
Using an electric mixer or a stand mixer, combine the eggs, sugar, butter, and vanilla extract on medium speed for about 2 minutes until light and fluffy.
Add the flour mixture 1/4 cup at a time and combine slowly until mixed.
Using a cookie scoop or a tablespoon, scoop the cookies into equal-size balls and place them on a parchment paper-lined baking sheet about 1 inch apart.
Chill in the refrigerator for at least 30 minutes.
When ready to bake, preheat the oven to 350F, and then bake for 10 to 12 minutes.