Line an 8x8-inch baking dish with parchment paper, including up the sides.
To a large saucepan over medium heat, add sugar, butter, and evaporated milk. Mix to combine.
Bring the mixture to a boil. Leave on heat until the mixture registers 234°F on a candy thermometer (about 5 minutes).
Remove from heat. Add chocolate chips, stirring until melted and thoroughly combined.
Add the mini marshmallows, vanilla extract, and peppermint extract, stirring until the marshmallows have melted. Gently fold in about ½ of the crushed peppermint candies, reserving the rest for the top.
Transfer the fudge to the prepared pan. Sprinkle the reserved peppermint candies on top.
Allow the fudge to set at room temperature (about 4 hours). To speed up the setting process, you can let it chill in the refrigerator to set (about 2 hours).
Serve at room temperature.