Preheat the oven to 350°F (175°C). Grease a 9x13-inch pan and set aside.
In a saucepan over medium heat, melt the butter with the brown sugar, stirring constantly until smooth.
Remove the pan from heat and stir in 1/2 cup peanut butter until fully combined; set aside to cool slightly.
In a large bowl, whisk together the flour, baking powder, baking soda, and salt.
Beat the eggs into the cooled peanut butter mixture one at a time, mixing well after each addition, then stir in 1 teaspoon vanilla.
Pour the wet mixture into the dry ingredients and stir until a smooth batter forms, then fold in the diced apples.
Spread the batter evenly in the prepared pan and bake for 30 minutes, or until the top is golden and edges are set.
Remove the bars from the oven and transfer the pan to a wire rack to cool while you make the glaze.
Whisk the sifted powdered sugar, 1/4 cup milk, 1/4 cup peanut butter, and 1/2 teaspoon vanilla together in a medium bowl until smooth.
Drizzle the glaze over the cooled bars, allow the glaze to set, then cut into 24 bars and serve.