In a shallow dish, sift the cornstarch, 1 teaspoon pepper and 1 teaspoon salt together. Toss the cubed tofu in the cornstarch mixture to coat.
Heat 1 inch of canola oil in a large skillet. When hot, add the tofu, being careful not to crowd the pan, and cook until golden brown and crisp on all sides. Drain the tofu on a paper towel-lined plate.
In a small saucepan, heat the soy sauce, honey and sesame oil. Bring to a boil and cook, stirring, for 3 minutes, until the honey is dissolved. Pour into a small bowl.
Return the small saucepan to the stove with the lo mein side sauce ingredients. Bring to a simmer, stirring. Remove from the heat.
Bring a large pot of salted water to a boil for the noodles. Add the noodles, stirring to prevent clumps. Cook according to package instructions, strain and return to the pot, drizzled with oil to prevent sticking.
In a large skillet or wok, heat the canola oil over high heat. Add the peppers, snow peas, bok choy, cabbage, carrots, mushrooms, broccoli, garlic, and mirin and cook, stirring quickly, until crisp-tender. Pour in the sauce from the small bowl, fried tofu and noodles and toss to coat.
Divide between plates to serve with side sauce.