Step 1: In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
Step 2: In a large bowl, cream together the softened butter and 1 1/2 cups of the granulated sugar until light and fluffy, about 2-3 minutes. Beat in the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
Step 3: Gradually add the dry ingredients to the wet ingredients, alternating with the buttermilk, beginning and ending with the dry ingredients. Mix until just combined. Do not overmix.
Step 4: Cover the dough and refrigerate for at least 1 hour, or until firm enough to roll. This helps prevent spreading.
Step 5: Preheat your oven to 375°F (190°C). Line baking sheets with parchment paper.
Step 6: Scoop rounded tablespoons of dough and roll them into balls. Place them about 2 inches apart on the prepared baking sheets. Sprinkle the remaining 1/4 cup of granulated sugar over the tops of the cookies.
Step 7: Bake for 10-12 minutes, or until the edges are lightly golden and the centers are just set. Do not overbake. While cookies are baking, prepare the glaze.
Step 8: For the glaze: In a small saucepan, combine the butter, 1/4 cup granulated sugar, and water. Bring to a simmer over medium heat, stirring until the sugar dissolves and the butter melts. Remove from heat and stir in the vanilla extract.
Step 9: As soon as the cookies come out of the oven, use a pastry brush or spoon to generously drench each warm cookie with the hot butter glaze. Let the cookies cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely. The glaze will soak in and set.