Preheat the broiler.
Line a baking sheet with aluminum foil, and spray lightly with nonstick cooking spray. Evenly space the marshmallows on the baking sheet.
Place marshmallows under the broiler and watch carefully. Once browned and toasted, immediately remove them from the oven. Flip the marshmallows over so that the white un-toasted side is facing up, then return to the oven until toasted.
Chill the toasted marshmallows in the refrigerator until room temperature--about 15-20 minutes.
Once cooled, put the marshmallows into a blender (or a food processor, like I did), add the cream/milk, then blend until completely smooth. Add the ice cream and continue blending until combined.
Pour milkshake into a freezer-safe container and chill in the freezer while you prepare the glasses. OR, if you don't feel like being fancy schmancy, go ahead and drink up!