Line an 8x8 inch square baking pan with parchment paper, leaving an overhang for easy removal.
Heat-treat the dry sugar cookie mix by microwaving it in a bowl for 60 seconds, stirring every 15 seconds, until the internal temperature reaches 160°F (71°C).
In a large heavy-bottomed saucepan over medium-low heat, combine the white chocolate chips and sweetened condensed milk.
Stir constantly until the chocolate is completely melted and the mixture is smooth.
Remove from heat and immediately stir in the heat-treated sugar cookie mix and cubed butter until the butter is fully incorporated.
Fold in the vanilla extract and half of the rainbow sprinkles.
Transfer the mixture to the prepared baking pan and smooth the top with an offset spatula.
Garnish with the remaining sprinkles, pressing them lightly into the fudge.
Refrigerate for at least 2 hours or until the fudge is completely firm.
Lift from the pan using the parchment overhang and slice into 1-inch squares.