Using a 2-tablespoon cookie scoop, dollop scoops of ice cream onto a pan lined with parchment paper. Place the ice cream into the freezer.

In the meantime, whisk the glutinous rice flour with the sugar. Pour in the water and mix until smooth.

Cover the bowl with plastic wrap and microwave for 1 minute. Stir the mixture, cover it, then microwave for 1 minute. Mix once again, then microwave for 30 seconds (it will be very sticky).

Place a large sheet of parchment paper onto a work station and dust it heavily with cornstarch. Carefully transfer the mochi dough from the bowl to the parchment square, as it will be hot.

Heavily dust the top of the mochi with cornstarch and roll it out to ¼'' thickness. Transfer the sheet of parchment with the rolled out dough to a pan and refrigerate for 30 minutes.

Take the mochi out of the fridge. With a cookie cutter of a 3-inch diameter, cut out circles from the dough. Cut squares of plastic wrap large enough to wrap the mochi in later and set aside.

Working one at a time, make the mochi. Hold a circle of dough in one hand, then place a ball of ice cream into the center of the circle. Working quickly, bring the mochi dough up and over the ice cream, pinching to seal. Place the mochi into a square of cling film and wrap it tightly. Immediately put the mochi into the freezer and repeat with the remaining mochi.

Once formed, let the mochi set in the freezer for at least an hour. Allow to thaw slightly before eating. Mochi ice cream will keep in the freezer for up to 3 months.