Line a 9-inch square baking pan with parchment paper, ensuring the paper extends slightly beyond the edges to allow easy removal of the finished fudge.

In a medium mixing bowl, combine the peanut butter, melted butter, vanilla extract, and powdered sugar. Using an electric mixer, blend the mixture until it is thoroughly combined and forms a crumbly, moldable texture.

Using clean, lightly greased or powdered hands, roll the mixture into 1-inch balls. Arrange the balls evenly within the prepared baking pan. Place the pan in the refrigerator to chill while preparing the chocolate layer.

Place the chocolate chips, sweetened condensed milk, and room-temperature butter into a heatproof or glass bowl. Set the bowl over a saucepan of gently simmering water, ensuring the bottom of the bowl does not touch the water. Stir continuously until the chocolate and butter have melted and the mixture becomes smooth and glossy.

Carefully pour the warm chocolate mixture over the chilled peanut butter balls, ensuring the chocolate spreads evenly and fills the spaces between the balls.

Refrigerate the assembled fudge until fully set. Once firm, lift the fudge from the pan using the parchment paper, transfer it to a cutting board, and slice it into 1-inch cubes. Serve as desired.