Pour 1 1/2 cups orange juice and 1 1/2 cups root beer into separate ice cube trays; freeze overnight. The next day, place a medium bowl and four 12-oz. clear glasses in the freezer to chill.
Preheat the broiler and position a rack in the top third of the oven. Line a baking sheet with nonstick foil and spread out the marshmallows to top making sure they don't touch each other. Broil until golden, about 1 minute. Remove and let cool on the baking sheet for about 30 minutes.
Using a blender, puree the remaining 1/4 cup orange juice and the frozen orange juice cubes until the mixture reaches a slushie consistency, stopping to stir with a spatula if needed. Transfer the slushie to the bowl in the freezer. Repeat the the remaining 3/4 cup root beer and the root beer cubes, leaving the root beer slushie in the blender.
Working quickly and using a spoon, fill one-quarter of each chilled glass with some of the root beer slushie. Top each with about 1/3 cup ice cream and sprinkle with 2 tbsp. marshmallows. Spoon in a layer of orange slushie, then another layer of ice cream. Sprinkle the remaining marshmallows on top. Serve immediately with long spoons, or freeze again for an hour before serving.