Let 1 pint of ice cream sit at room temperature to soften slightly, 5 to 10 minutes.
Line a baking sheet or egg carton with plastic wrap. Scoop out 2 tablespoons ice cream (about 1 ounce) with 2 spoons or a 2-tablespoon ice cream scoop, and shape into a tight ball. Place on the baking sheet or in a well in the egg carton. Repeat until you have 8 balls. Freeze until solid, about 4 hours.
Place 1 cup glutinous or sweet rice flour, 1 cup water, and ¼ cup granulated sugar in a medium microwave-safe bowl. If using, add in 1 drop gel food coloring (green for matcha, red for strawberry). Using a damp flexible spatula, mix until combined – the mixture will be lumpy and the sugar will not be fully dissolved.
Cover the bowl with plastic wrap and microwave on high for 1 minute. Fold over the mixture with the spatula, scraping down the sides. Microwave on high for 1 minute more.
Dust a cutting board generously with cornstarch. Dust a work surface with cornstarch. Transfer the mochi dough onto the work surface. Sprinkle the top lightly with more cornstarch. Using a rolling pin, roll out the dough into a 7x10-inch rectangle that’s ¼-inch thick, dusting with more cornstarch as needed if sticky. Transfer to the cutting board and refrigerate until firm, about 30 minutes.
Using a large knife or pizza cutter, cut the dough into 8 even rectangles (about 2 ½ x 3 ½-inches each). Brush off any excess cornstarch. Line a plate with plastic wrap, then stack the dough pieces on the plate with a sheet of plastic wrap in between each one. Cover the top piece loosely with plastic wrap. Refrigerate for 30 minutes.
Assemble the mochi ice creams: Have a baking sheet ready. Place the mochi rectangles on the work surface, keeping the plastic wrap underneath. Place 1 ice cream ball in the center of 1 mochi rectangle. Work quickly, stretch the mochi over the ice cream until completely covered, then pinch the dough together tightly at the seam to seal.
Wrap the mochi ball with the plastic wrap and twist tightly to encourage extra sealing. Place the mochi ball on the work surface and very gently push down with the heel of your hand while moving your hand in 2 small circular motions, then gently cup the ball with both hands toward the end to form a flat round that’s about 2-inches thick.
Place on the baking sheet and transfer to the freezer. Repeat forming the remaining mochi ice creams. Freeze until firm, 3 to 4 hours. Let sit at room temperature for 3 to 5 minutes before serving.