Line a sheet pan with parchment paper. Use a small ice cream scoop to tightly pack and scoop ice cream balls onto the parchment. Freeze for 1 hour.
In a microwave-safe bowl, combine glutinous rice flour, sugar, and powdered sugar. Stir in water until smooth.
Cover with plastic wrap and microwave for 1 minute. Wet a spatula, fold the mixture, cover, and microwave for another minute.
Fold and microwave an additional 30 seconds until shiny. Microwave for 30 more seconds if needed.
Dust parchment paper with cornstarch. Transfer hot mochi dough to parchment, dust with more cornstarch, and roll into a rectangle about ¼ inch thick.
Refrigerate for 30 minutes.
Remove dough from the fridge. Cut circles about 3 inches in diameter.
Brush off excess cornstarch, place an ice cream ball in each circle, and pinch the dough around the ice cream to seal.
Wrap in plastic wrap, twisting tightly.
Place wrapped mochi in the freezer, seam side down, for at least 1 hour.
Store in a freezer-safe bag or container for up to 3 months. Allow to thaw slightly before eating.