How to Make It
In a blender, combine the strawberries with the jam and pulse until smooth, about 2 minutes; you should have 1/2 cup.
Using a damp cloth, wipe down a large work surface. Stretch a 14-inch sheet of plastic wrap over the surface and use the damp cloth to smooth it out. Sift a generous layer of cornstarch over the plastic wrap. Dust a large rimmed baking sheet with cornstarch.
In a large microwave-safe bowl, mix the rice flour with the water, sugar, strawberry puree and salt. Cover the bowl tightly with plastic wrap. Microwave the mochi mixture at high power for 2 minutes, until the batter starts to thicken at the edges. Remove the plastic wrap and, using a rubber spatula, stir the mixture until it is mostly smooth; a few small lumps are OK. Cover the bowl with the plastic wrap and microwave at high power for another 2 minutes; the dough should be stiff and sticky. Using a rubber spatula, stir the dough quickly and vigorously until smooth, about 30 seconds.
Working quickly, scrape the mochi dough out onto the prepared work surface and sift a fine layer of cornstarch over it. Pat the dough into a 9-inch round. Using a rolling pin lightly dusted with cornstarch, roll out the dough 1/4 inch thick.
Dip a 2-inch round cutter in cornstarch and stamp out 24 rounds, rerolling the scraps as needed. Transfer the mochi to the prepared baking sheet. Cover with plastic wrap and freeze until firm, about 1 hour.
Meanwhile, scrape the softened ice cream into a gallon-sized resealable freezer bag. Using a small spatula, spread the ice cream evenly so it's about 3/4 inch thick in the bag, then squeeze out any excess air and seal. Freeze until firm, about 1 hour.
Line a 12-cup muffin tin with paper or foil liners. Using a pastry brush, dust the excess cornstarch off the mochi rounds. Place 1 mochi round in each cup. Lay the bag of ice cream flat on the counter and snip around the top of the bag, then peel it off. Using a 2-inch round cutter, stamp out 12 rounds of ice cream. Working quickly, lightly brush the 12 mochi in the muffin cups with water and top with the ice cream rounds. Brush each of the remaining 12 mochi rounds with water and set them damp side down on the ice cream. Press lightly to help the mochi and ice cream stick together. Freeze until firm, about 1 hour. Let the mochi sandwiches soften for about 10 minutes before serving.