Line an 8×8-inch baking dish with parchment paper. Make sure the parchment extends up the sides for easy removal.
In a large microwave-safe bowl, combine 1 ½ cups semi-sweet chocolate chips, milk chocolate chips, sweetened condensed milk, hot chocolate mix, and butter. Microwave in 30-second increments, stirring well after each, until the chocolate is completely melted and smooth (about 2-3 minutes).
Stir in the vanilla and mix well.
Fold in 2 cups of the miniature marshmallows. Microwave for 20 to 30 seconds, then stir gently 2 to 3 times to soften the marshmallows slightly.
Pour the mixture into the prepared baking dish and smooth the top into an even layer.
Top with the remaining miniature marshmallows. Gently press them down so they stick.
Cover with plastic wrap and refrigerate for at least 2 hours, or until firmly set.
Once set, remove the fudge from the pan using the parchment overhang.
Combine the remaining ½ cup semi-sweet chocolate chips and vegetable oil in a small microwave bowl. Microwave in 15-second intervals, stirring after each, until smooth.
Drizzle the melted semi-sweet chocolate over the marshmallows and let sit for a few minutes until the chocolate sets. Slice and serve!