Scoop ice cream into 10 small balls, place on a parchment-lined tray, and freeze until rock hard, at least 1 hour.

Whisk mochiko and sugar in a microwave-safe bowl, stir in water until smooth, cover loosely, and microwave on high for 1 minute, stir, then microwave another minute until glossy and translucent.

Dust a surface generously with cornstarch, transfer the hot dough, dust the top, and roll out to about 1/8 inch thick.

Cut 3-inch circles, place a frozen ice cream ball in the center of each, wrap the dough up and around it, and pinch to seal seam-side down.

Freeze the wrapped mochi on a plate for at least 2 hours until solid, then serve straight from the freezer.