In a microwave safe bowl, add the white chocolate chips, sweetened condensed milk and butter. Microwave on high for 1 minute increments, stopping to stir. Continue to melt and stir. When chips are completely melted, add the peppermint extract and food coloring. Stir thoroughly until fudge is completely smooth and color is evenly distributed.
Refrigerate or freeze fudge until ready to serve. As the fudge comes to room temperature it can become sticky. It is helpful to serve the fudge in mini-muffin liners.