Preheat the oven to 350°F (175°C) and line or grease an 8x8-inch baking pan.
In a mixing bowl, combine 1 tablespoon melted unsalted butter, 1/2 cup peanut butter, 1/2 cup granulated sugar, 1/2 cup brown sugar, and 2 large eggs; whisk until smooth.
Stir in 1 teaspoon vanilla extract (or cooled coffee), then add 1 cup all-purpose flour, 1 teaspoon baking powder, and 1/2 teaspoon salt; mix until just combined.
Pour the batter into the prepared pan and spread it evenly.
Bake for about 25 minutes, until the top is set and a toothpick inserted near the center comes out mostly clean; remove from oven and let the bars cool slightly while you make the glaze.
For the glaze, melt 2 tablespoons butter and 4 tablespoons peanut butter together in a microwave-safe measuring cup or small bowl; whisk until smooth.
Add 1/2 teaspoon vanilla extract (or cooled coffee) and whisk, then add 1 cup powdered sugar and whisk until the glaze is smooth and spreadable.
If the glaze is too thick, add a splash of milk and whisk to reach a spreadable consistency.
Spread the glaze over the warm bars, then let the bars cool completely until the glaze sets before cutting into 15 bars.