Line your 9x9 inch pan with parchment paper to prevent sticking and for easy removal.
Place the butter and peanut butter in a microwave-safe bowl and microwave in 30-second bursts, stirring each time until the mixture is completely smooth and bubbly—this fills the kitchen with a warm, nutty aroma.
Add the honey and vanilla extract to the melted mixture, then stir well until everything is evenly combined and has a glossy, smooth appearance.
Pour the mixture into your prepared pan, and use a spatula to press it into an even layer, making sure to push it into the corners for a uniform thickness.
Place the pan in the fridge and chill for at least 2 hours, or until the mixture is firm and the surface feels solid to the touch—this helps the bars set up perfectly.
Once chilled and firm, lift the bars out of the pan using the parchment paper and place on a cutting board. Use a sharp knife to cut into squares, wiping the blade clean between cuts for crisp, neat edges.
Serve immediately or store in an airtight container in the fridge for up to a week. These bars are best enjoyed chilled, with a chewy texture and a rich peanut buttery flavor.