In a large microwave-safe bowl, whisk together the sweet rice flour, matcha powder, and sugar until the matcha is evenly distributed with no clumps.
Add the water and vanilla extract, whisking until completely smooth with no lumps remaining. The mixture should have the consistency of thin pancake batter.
Cover the bowl loosely with plastic wrap, leaving one corner open for steam to escape. Microwave on high for 2 minutes.
Remove and stir vigorously with a wet spatula, then microwave for another 1 minute. The mixture should be glossy, stretchy, and mostly translucent.
Dust a clean work surface generously with potato starch. Turn the hot mochi dough out onto the surface and dust the top as well.
Let cool for 3-4 minutes until safe to handle. Wet your hands with water, then gently stretch and fold the dough 2-3 times to create a uniform texture.
Using wet hands, divide the dough into 12 equal portions (about 2 tablespoons each). Roll each portion into a smooth ball, dusting with starch as needed.
Place finished mochi on a parchment-lined plate. Let them sit for 10 minutes to set the exterior before serving or storing.
