Preheat your oven to 350°F and line your baking sheets with parchment paper.

In a mixing bowl, cream together the softened unsalted butter and the granulated and powdered sugars until the mixture turns light and fluffy.

Add the eggs and both vanilla and butter extracts, blending them into the creamed mixture until well combined.

In a separate bowl, sift together the all-purpose flour, baking powder, and salt. Gradually incorporate these dry ingredients into the wet mixture, blending until just combined.

Use your hands to form small balls of dough and place them on the lined baking sheets, slightly flattening each ball.

Bake the cookies for about 10 to 12 minutes, or until the edges are golden brown. Keep an eye on them to ensure they remain slightly soft in the center.

While the cookies are baking, prepare the glaze by melting the butter in a small saucepan. Stir in the granulated sugar and water until dissolved, then blend in the vanilla extract.

After removing the cookies from the oven, brush them generously with the warm glaze while still warm.

Allow the cookies to cool completely on a wire rack.