Bring a pot with water over medium heat to a boil. Prepare a small bowl of ice water.
Meanwhile, mix rice flour and sugar for dough in a bowl until well blended. Add water, 1 tablespoon at a time, stirring well after each addition, until dough is squishy but firm.
Dust a work surface with cornstarch. Set dough on top and knead until smooth. Pull off small amounts of dough and roll into small, uniform balls (dumplings). Use up all the dough this way.
Drop a handful of rice dumplings into the boiling water at a time. Cook until dumplings rise to the top, 3 to 5 minutes. Once they have risen to the top, cook for 2 more minutes. Remove with a slotted spoon and immediately drop them into the bowl of ice water.
Remove dumplings from the ice water and thread 3 to 4 a skewer. Repeat with remaining dumplings, adding more ice to the water for the cooling stage once as needed.
Prepare sauce: Combine 1 cup water, sugar, and soy sauce in a saucepan over medium heat. Cook until sugar dissolves. Stir together cornstarch and 1 1/2 tablespoons water in a small bowl and add to the soy sauce mixture. Cook, stirring, until sauce thickens, then remove from heat and cool slightly.
Heat a griddle over medium heat. Once hot, grill skewered dumplings on both sides until lightly browned, about 3 minutes. Remove to a plate and pour cooled mitarashi sauce on top. Serve.