In a large mixing bowl, combine the sweet rice flour and granulated sugar. Mix well to ensure the sugar is evenly distributed.
Gradually add the milk and vanilla extract to the dry ingredients, stirring until the mixture is smooth and free of lumps.
Grease a microwave-safe dish with the unsalted butter. Pour the mochi mixture into the dish and spread it evenly.
Cover the dish with plastic wrap, leaving a small vent for steam to escape. Microwave on high for 2 minutes.
Carefully remove the dish from the microwave (it will be hot) and stir the mixture. Cover and microwave for an additional 2 minutes.
Remove the dish again, stir, and microwave for another 1-2 minutes until the mochi is thick and slightly translucent.
Let the mochi cool for about 10 minutes. Dust a clean surface with cornstarch and turn the mochi out onto it.
Cut the mochi into squares or desired shapes, dusting each piece with cornstarch to prevent sticking.