Preheat your oven to 400°F (200°C) and prepare a large cookie sheet with a bit of butter or line it with parchment paper.

In a mixing bowl, whisk together the all-purpose flour, sugar, baking soda, and salt until combined.

In another bowl, beat the eggs, milk, and vanilla extract together until smooth and slightly frothy.

In a saucepan over medium heat, melt the unsalted butter and peanut butter until reaching a rolling boil; then remove from heat.

Pour the melted butter mixture into the dry ingredients, followed by the milk-egg mixture. Stir until just combined.

Spread the batter evenly onto the cookie sheet and bake for about 20 minutes, until the edges are golden brown.

Once baked, let the bars cool completely in the pan before frosting.

In the same saucepan, warm the unsalted butter and peanut butter until boiling again, then mix in milk and powdered sugar until smooth.

Spread the frosting generously over the cooled bars. Allow to set before slicing them into squares.

Optional: Top with chopped peanuts or a drizzle of chocolate for extra flavor.