Add the sweetened condensed milk, chocolate chips, butter, and vanilla to a medium saucepot.
Heat the ingredients over medium-low, stirring constantly, until everything is melted and evenly combined. The mixture will be quite thick and glossy when it's ready (see photos below).
Spread the fudge into a 8x8-inch pan lined with foil or parchment paper. Sprinkle the chopped nuts over top and press them lightly into the surface.
Place the fudge in the refrigerator, uncovered, for about two hours or until fully chilled and firm. Remove the fudge from the refrigerator and slice into 16 pieces, then serve.