Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.
In a large mixing bowl, cream together the softened butter and 1 cup of granulated sugar with an electric mixer until the mixture is light and fluffy, about 2-3 minutes.
Beat in the eggs one at a time, followed by the vanilla extract, scraping down the sides of the bowl to ensure everything is fully incorporated.
In a separate medium bowl, whisk together the flour, baking powder, and salt until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed just until a soft dough forms and no streaks of flour remain; avoid overmixing.
Place the 1/4 cup of granulated sugar for rolling in a small bowl. Scoop about 1 1/2 tablespoons of dough, roll it into a ball between your palms, then roll it in the sugar to coat completely.
Place the sugared dough balls about 2 inches apart on the prepared baking sheets and gently flatten each ball slightly with the bottom of a glass or your fingers.
Bake for 8-10 minutes, or until the edges are just set and the bottoms are lightly golden; the centers should still look soft. Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.