In a medium saucepan over medium heat, combine sweetened condensed milk, chocolate chips, and peanut butter. Stir constantly with a silicone spatula or wooden spoon until the chocolate is melted and the mixture is smooth and glossy.

Remove the pan from heat. Add butter and vanilla extract, stirring until the butter is completely melted and fully incorporated.

Serve warm over ice cream, brownies, or cake. Let the fudge cool completely before transferring to a sealed glass jar or airtight container. Store in the refrigerator for up to 2 weeks. Reheat gently before serving.