Cream the softened butter and sugar in a large mixing bowl using a hand or stand mixer until the mixture is pale and airy, about one minute. Blend in the eggs and vanilla extract until fully combined and fluffy. This step ensures the cookies have a tender crumb and a rich flavor.
In a separate bowl, sift together the flour, baking powder, and salt to remove any lumps and evenly distribute the leavening agent. Gradually incorporate the dry ingredients into the butter mixture, mixing on low speed or stirring gently until just combined. Avoid overmixing to ensure your cookies remain soft and tender.
Cover the dough with plastic wrap and refrigerate for 30 minutes. This chilling process firms up the dough, making it easier to handle and enhancing the cookies' flavor.
While the dough chills, preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper and set it aside.
Once the dough is chilled, scoop portions using a medium-sized cookie scoop or roll into 1.5-inch balls by hand. Arrange the dough balls on the prepared baking sheet, leaving about 2 inches of space between each. For a flatter cookie ideal for frosting, gently press the dough balls down with a flour-dusted glass or your fingers. Otherwise, bake as-is for a more domed appearance.
Bake for 10–12 minutes, or until the tops are set and the edges show the faintest hint of golden color. Timing may vary depending on your oven and the size of your cookies. Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.