**Preheat Oven:**

Preheat your oven to 350°F (175°C) and line baking sheets with parchment paper.

**Make the Cookie Dough:**

In a large bowl, beat softened butter, granulated sugar, and powdered sugar until light and fluffy. Add eggs one at a time, mixing well after each addition. Stir in vanilla extract. In a separate bowl, whisk together flour, baking powder, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until combined.

**Scoop and Bake:**

Scoop dough into 1 1/2-inch balls and place them on the prepared baking sheets, spacing them about 2 inches apart. Bake for 10-12 minutes, or until the edges are lightly golden. Remove from the oven and let cool on the baking sheet for 5 minutes before transferring to a wire rack.

**Prepare the Glaze:**

While the cookies cool, make the glaze. In a small saucepan, melt butter over medium heat. Stir in granulated sugar and water, cooking until the sugar is dissolved and the mixture begins to bubble gently. Remove from heat and stir in vanilla extract.

**Glaze the Cookies:**

Using a spoon, drizzle the warm glaze over each cookie, allowing it to soak in slightly. Let the cookies cool completely so the glaze sets.