Bring a large pot of water to a boil. Add a pinch of kosher salt and soba noodles, Stir well and cook until just done, about 4 minutes. Drain in a colander and rinse under cool water to stop the cooking. Drain well and return back to the pot. Add sesame oil and stir to coat. You can do this in advance.

Slice tofu into three equal slabs. Press each slab with a paper towel to absorb excess moisture. This will make the tofu able to absorb other flavors. Cut into 1-inch cubes.

In a small bowl, whisk together arrowroot, rice wine, shoyu, and water. Set aside.

Heat 1 Tablespoon oil over medium high heat in a wok or large skillet and swirl around the sides of the wok. Add the red pepper flakes, garlic, ginger and scallions. Cook, stirring, until fragrant, about 1 minute. Add the tofu and stir-fry until lightly colored, about 5 to 6 minutes. Don't move it around too much, otherwise it will stick.

Add the remaining tablespoon of oil along with the cabbage and mushrooms and sprinkle with a pinch of salt. Stir-fry one minute until just wilted, but not cooked all the way.

Give the reserved sauce a quick whisk and then add to the wok along with the noodles. Stir-fry, tossing constantly to heat through. You can remove the garlic and ginger before serving, if desired.