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

Cream together softened butter with granulated and powdered sugars until light and fluffy, about 3-4 minutes. Add in eggs, vanilla, and butter extract, mixing until smooth.

In another bowl, gently whisk together flour, baking powder, and salt. Fold these dry ingredients into the butter mixture until just combined.

Shape the dough into 1.5-inch balls, placing them on baking sheets about 2 inches apart, and flatten each ball slightly.

Bake for 10-12 minutes, until edges are golden brown and centers remain soft.

In a small saucepan, melt 4 tablespoons of butter over low heat. Stir in granulated sugar and water until dissolved, then add vanilla extract.

Brush or drizzle the glaze over warm cookies right out of the oven, allowing it to soak in.

Transfer glazed cookies to a wire rack to cool completely.