Preheat the oven to 350°F (175°C). Line baking sheets with parchment paper.

In a large bowl, cream 1 cup softened butter with 1 cup granulated sugar and ½ cup powdered sugar until light and fluffy, about 2 to 3 minutes.

Beat in the eggs one at a time, scraping the bowl between additions. Stir in 1 tsp vanilla and 1 tsp butter extract if using.

In a separate bowl, whisk together 2.5 cups flour, 1 tsp baking powder, and ¼ tsp salt.

Fold the dry ingredients into the wet just until combined. Avoid overmixing to keep the cookies tender.

Scoop uniform balls of dough (about 1.5 tablespoons each) and place them on the prepared sheets, spacing them about 2 inches apart.

Flatten each ball slightly with your palm or the bottom of a glass.

Bake for 10 to 12 minutes, or until the edges are lightly golden but centers still look soft.

While the cookies bake, make the glaze by melting ½ cup butter in a small saucepan. Add ¾ cup granulated sugar and ¼ cup water; stir over low heat until sugar dissolves and mixture is smooth.

Remove from heat and stir in 1 tsp vanilla extract.

When the cookies come out of the oven, brush the warm glaze over the top of each cookie so it soaks in.

Let cookies cool on the sheet until set, then transfer to a cooling rack to finish cooling completely.