Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper or lightly grease it for easy cleanup.
In a large mixing bowl, use a hand mixer or stand mixer to cream the softened butter and sugar together until light and fluffy. This should take about 2–3 minutes on medium speed.
Beat in the eggs one at a time, ensuring each egg is fully incorporated before adding the next. Mix in the vanilla extract.
In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients, mixing on low speed just until combined. Be careful not to overmix.
Use a cookie scoop or tablespoon to drop rounded portions of dough onto the prepared baking sheet, spacing them about 2 inches apart. Flatten each ball slightly with the back of a spoon or your fingers.
Bake the cookies in the preheated oven for 10–12 minutes, or until the edges are lightly golden but the centers are still soft. Avoid overbaking to keep them tender.
While the cookies are baking, make the glaze. In a small saucepan over low heat, combine the butter, sugar, water, and vanilla extract. Stir continuously until the butter melts and the sugar dissolves. Remove from heat and set aside.
As soon as the cookies come out of the oven, brush the warm glaze generously over each cookie, allowing it to soak in. Repeat until all the glaze is used. Let the cookies cool on the baking sheet for 5–10 minutes before transferring them to a wire rack.
