Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper or silicone baking mats.
In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy.
Beat in the eggs, one at a time, then add the vanilla extract.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the butter mixture, alternating with the buttermilk, beginning and ending with the dry ingredients. Mix until just combined.
Drop rounded tablespoons of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden. Allow the cookies to cool on the baking sheets for a few minutes before transferring them to a cooling rack to cool completely.
In a small saucepan, melt the butter over medium heat. Stir in the granulated sugar and water, and bring the mixture to a boil.
Remove from heat and stir in the vanilla extract.
While the cookies are still warm, spoon the glaze over the tops of the cookies, allowing it to soak in.
Let the glazed cookies cool completely on the cooling rack.