Line an 8x8 inch square baking pan with parchment paper, ensuring excess paper hangs over the edges for easy removal.
In a large microwave-safe bowl, combine the butter and creamy peanut butter. Heat in 30-second increments, stirring between each, until completely melted and homogenous.
Stir the vanilla extract into the peanut butter mixture.
Gradually incorporate the powdered sugar into the peanut butter mixture, stirring until a thick, uniform dough forms.
Press the peanut butter mixture firmly and evenly into the bottom of the prepared baking pan using a spatula or the bottom of a measuring cup.
In a separate microwave-safe bowl, combine the semi-sweet chocolate chips and the sweetened condensed milk.
Heat the chocolate mixture in 30-second intervals, stirring thoroughly after each interval, until the chocolate is fully melted and the texture is glossy.
Pour the chocolate ganache over the peanut butter layer, spreading it to the edges with an offset spatula to create an even surface.
Refrigerate the fudge for at least 2 hours, or until the layers are completely set and firm to the touch.
Grasp the parchment paper overhang to lift the fudge from the pan and slice into 1-inch squares using a sharp knife.