Line an 8×8 inch pan with parchment paper and spray with non-stick cooking spray. Set it aside.
Prepare the crust by placing the Oreo Cookies into a food processor. Process them until they turn into a fine crumb.
Add the butter to the cookie crumbs and process again for an additional 5 to 10 seconds.
Pour the cookie crust mixture into the lined pan and press it out evenly across the bottom.
In a medium saucepan, combine the butter, miniature marshmallows, and sweetened condensed milk. Cook on medium-low heat while stirring continuously.
Watch carefully as the marshmallows melt; you want them to combine well without burning. Stir until completely smooth and well combined.
Remove the saucepan from the heat, and stir in the white chocolate chips.
Add the peppermint extract and mix well to distribute the minty flavor throughout the fudge.
Pour half of the fudge mixture over the prepared crust in the pan. Use a spatula to smooth it out evenly.
For the remaining fudge, add a few drops of red food coloring at a time. Stir it in until you achieve the desired color. Pour this red fudge layer over the white fudge and smooth it out.
Immediately sprinkle with your choice of toppings, such as crushed candy canes or festive sprinkles, to finish off the look.
Place the pan in the refrigerator until the fudge is set, which usually takes about 30 minutes to 1 hour. Once set, remove from the pan and cut into one-inch pieces for serving.