In a large mixing bowl, combine the sweet rice flour, milk, sugar, and vanilla extract. Whisk until smooth and there are no lumps.

Transfer the mixture to a microwave-safe bowl. Cover it loosely with a microwave-safe lid or plastic wrap, leaving a small gap for steam to escape.

Microwave on high for 1 minute. Remove and stir well. Return to the microwave and cook for another minute. Stir again, then microwave for an additional 30 seconds. The mixture should be thick and slightly sticky.

Dust a clean surface with cornstarch. Pour the mochi mixture onto the surface and let it cool for about 10 minutes.

Once cool enough to handle, dust your hands with cornstarch and knead the mochi gently for a minute. Divide the dough into small pieces (about 1 inch each) and shape them into balls or flatten them into discs.

Dust the finished mochi pieces with more cornstarch to prevent sticking.

Serve immediately or store in an airtight container in the refrigerator for up to 3 days.