Toast the potato starch in a dry skillet over medium heat for 2-3 minutes, stirring constantly, until it smells slightly nutty and turns off-white. Set aside to cool.
In a microwave-safe bowl, whisk together the sweet rice flour, sugar, and salt until no lumps remain.
Add the water, almond extract, and vanilla extract to the bowl, whisking vigorously until the mixture is completely smooth with no dry pockets of flour.
Cover the bowl loosely with plastic wrap and microwave on high for 2 minutes. Remove and stir thoroughly with a wet spatula.
Microwave for another 1 minute, then stir again. The mixture should be translucent and very sticky, pulling away from the sides of the bowl. If still opaque, microwave in 20-second bursts until fully cooked.
Dust a clean work surface generously with the toasted potato starch. Turn the hot mochi dough out onto the starch and dust the top heavily.
Let cool for 2-3 minutes until safe to handle, then knead gently 5-6 times while still warm, adding more starch as needed to prevent sticking.
Roll the dough into a log and cut into 8 equal portions using a bench scraper or knife dusted with starch.
Shape each portion into a smooth round or square, rolling in starch to coat completely. Dust off excess starch before serving.