Heat 1 teaspoon of oil and one tablespoon of tamari in large pan or wok over medium-high heat. Stir-fry the tofu for about 10 minutes, or until golden brown on all sides. Transfer to a plate and set aside.
In a large pan or wok, cook the ginger and garlic in the remaining oil over medium-high heat for about a minute.
Add the carrot, broccoli and mushrooms. Cook, stirring frequently until the broccoli turns bright green and the mushrooms start to soften, for about 5 minutes.
While the vegetables are cooking, mix together the toasted sesame oil, red pepper flakes, apple cider vinegar, remaining tamari, and cornstarch.
Add the sauce mixture, noodles, tofu and scallions to the pan. Cook for another 5 minutes or, stirring frequently, to allow the noodles to absorb the sauce.
Remove from heat and top with sesame seeds and sriracha, if using.