Press each fried tofu square using a rolling pin to flatten. Place flour in a bowl and toss tofu in the flour. Season with salt and pepper.
Heat olive oil in a skillet over medium-high heat. Add tofu and cook until golden brown, turning from time to time, 4 to 6 minutes. Set aside to cool while you prepare the rice.
Bring 4 cups salted water to a boil in a pot, add rice, cover, and reduce heat to low. Simmer until rice is tender, about 18 minutes. Remove from heat and fluff, draining any excess water. Stir in rice vinegar and additional salt. Keep warm.
Cut fried tofu squares in half and carefully open to make pouches.
Heat 1 cup water in a saucepan over medium heat; stir in sugar and soy sauce. Add tofu and cook until liquid has evaporated, 10 to 15 minutes. Remove tofu pouches and stuff with rice.
