Preheat the oven to 350F. Grease an 8x8 baking pan with butter and stick parchment paper to the bottom and sides.
In a large glass/porcelain mixing bowl, add butter and heat in microwave until melted. Add molasses, vanilla extract and espresso powder to the bowl and whisk until combined. Once butter is cooled enough to not cook the eggs, whisk them into the bowl, one at a time, until really well beaten. Add the brown sugar and again mix until well combined.
Place a sifter/metal sieve over the bowl and add the flour, baking soda and salt. Sift over the top of the mixing bowl into the wet ingredients. Stir until combined.
Pour half the batter into the bottom of the pre-lined baking pan. Using a spatula, add the peanut butter, spreading it to create a layer on top of the batter. Add the remainder of the batter over top and bake for 35-45 minutes or until a toothpick insert into the centre comes out clean. Let cool 10 minutes in the pan, before removing to a cooling rack and cutting into squares.