Place the cucumbers in a heatproof bowl. In a small saucepan, bring the rice vinegar, water, sugar, salt and chile flakes to a boil, stirring to dissolve the salt and sugar. Pour the hot liquid over the cucumbers and marinate overnight, or allow to cool fully to room temperature
Preheat the oven to 400°F.
Toss the tofu with chile sauce and 1 tablespoon oil on a baking sheet. Roast for 15-20 minutes, until beginning to brown. Toss halfway through.
Toss the mushrooms with the remaining oil on a second baking sheet and roast for 8-10 minutes, or until tender.
Bring a large pot of salted water to a boil. Add the noodles and cook according to package instructions. Drain, return to the pot and toss with sesame oil.
For the peanut dressing, mix all the ingredients together using an immersion blender or food processor. This can also be done by hand using a whisk, medium-sized bowl and some effort! Season to taste with salt and pepper.
To serve, divide the noodles between bowls. Top with chili tofu, roasted mushrooms, cherry tomatoes, peanut dressing, scallions, crushed peanuts and furikake.