When the ice cream balls are good and frozen, it's time to make mochi! In your microwave. In a microwave-safe bowl, whisk the flour and sugar. Add the water and whisk to combine.
Cover the bowl with plastic wrap and microwave for 1 minute. Using a wet rubber spatula, stir the mixture, then re-cover and microwave for 1 more minute. Stir again, cover, and microwave for 30 more seconds. The color should now be translucent.
Lay down a piece of parchment on your work surface, then use a fine-mesh sieve or sifter to cover it with the potato starch. Transfer the mochi to the parchment, sift over more starch, and wait for it to cool down enough to handle.
Using a rolling pin, roll the mochi out so that it's about ÂĽ inch thick, applying more starch as you need to. Transfer the parchment to a baking sheet and refrigerate for about 15 minutes, until firm and cool to the touch.
Now put on a pair of plastic gloves if you have them. Working preferably with one ice cream scoop at a time (and in close proximity to the freezer!), take a mochi circle, with the plastic wrap beneath it, place the ice cream on top, and move quickly to wrap and smoosh the mochi around it. Using the plastic wrap as a guide, tie everything together (I twist it very tightly at the seam to hold all the parts inside—almost like a harness!). Transfer the mochi ball to the freezer, then proceed until you've gone through all the ice cream. Freeze the balls for at least a couple of hours, until frozen solid. Before serving, let the mochi sit at room temperature for about 5 minutes, until the outer layer has returned to its soft, smooshy state.