Note: if Andes peppermint crunch baking chips are not available, Andes peppermint crunch thins can be used instead. Just unwrap and chop them up.
Fit a 9x9 baking dish with parchment paper and grease the paper all over the bottom and sides with some non-stick baking spray (or butter), so fudge doesn't stick.
Place white chocolate chips, 1/2 cup peppermint crunch baking chips, and marshmallow fluff in a large mixing bowl. Set aside.
In a bottom-heavy sauce pot, over medium heat, start melting butter and add sweetened condensed milk. Heat completely through over medium heat, stirring slowly but constantly so that condensed milk doesn't burn.
Pour hot condensed milk mixture into the bowl and slowly stir until all smooth. (You will want to start mixing slowly, so the hot mixture doesn't splatter on you, and then increase your stirring speed to get the mixture nice and smooth. If using a metal mixing bowl, you may want to hold it with an oven mitt while mixing. I recommend using a thin rubber spatula to mix.)
Pour fudge mixture into the prepared baking dish and spread it evenly. Let it cool for a few minutes and spread remaining Andes peppermint crunch baking chips over the top evenly. Press very gently and a little bit.
Let it stand on the counter until it cools to room temperature. Cover pan with saran wrap and place it in the refrigerator to chill and firm up for a 2-4 hours.