Preheat the oven to 375°F.
In a small pot, combine the sugar, soy sauce and shoyu. Bring to a boil and simmer for 10 minutes, stirring to dissolve the sugar.
On a baking sheet, toss the shiitakes, cabbage, daikon and snow peas with half of the yaki sauce, the canola oil and a big pinch of salt. Roast until crisp-tender, about 10-15 minutes.
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. Toss with the remaining yaki sauce.
To make the citrus dressing, combine all of the ingredients except the oil in a blender, food processor, or immersion blender. As the mixture is blending, slowly add the oil to emulsify. Season to taste with salt.
Divide the noodles between bowls and top with the roasted vegetables, citrus sauce, scallions and furikake to serve.