In a saucepan, heat the oil over medium-high heat. Stir in the mushrooms and sauté until soft and beginning to brown, about 3 minutes. Add the Marsala (be careful as the wine may flare up) and simmer until nearly evaporated. Whisk in the soy milk, sugar, broth and tofu. Bring the sauce to a boil, then reduce the heat to medium-high and simmer until reduced by half. Season with salt, pepper and garlic; keep warm while preparing the chicken.
Combine the rice and soy flours in a shallow dish. In another shallow dish, whisk the eggs together. Dip the chicken breasts first in the egg to coat, then dredge in the flour mixture to coat, shaking off the excess. Heat the oil in a large skillet over medium-high heat. Add the chicken and sauté on both sides until well-browned and cooked through, about 10 minutes, or until the internal temperature reaches 160°F on an instant-read thermometer. Serve chicken breasts immediately with warm Marsala sauce.