In a small bowl, stir together all the ingredients for the dressing and set aside.
In a large stock pot/saute pan, add 1 1/2 tablespoons of the canola oil. Heat over medium-high heat for a minute and add the sliced shitake mushrooms. Cook for 3-4 minutes, stirring occasionally until they start to shrink and lightly brown. Scoop mushrooms out of the pan into a small bowl and set aside.
In the same pan you used for the mushrooms, add the other 1 1/2 tablespoons of canola oil and the other chopped vegetables (broccoli, peppers, carrots). Stir to coat in oil and then cover. Cook for 5-7 minutes with the lid on, stirring occasionally. Heat until vegetables are crisp tender.
While your vegetables are cooking, heat a medium saucepan of water over medium heat. Once it starts to boil, add the soba noodles. Cook for 5 minutes and then drain. Toss noodles with the spiraled zucchini and pour the dressing over top. Toss to coat.
To assemble bowls, layer a serving of noodles into a bowl, top with vegetables and mushrooms. Serve with a slice of lime. For some added protein, add endamame or tofu.