Whisk together all the ingredients in a medium bowl. Set aside.
Make the salad
Cook the soba noodles in boiling water according to package directions (usually 7-8 minutes). Rinse with cold water and drain. Transfer to a large serving bowl.
Pour half the dressing over the noodles and toss gently. Add the cucumber, tomatoes, red bell pepper, green onions and basil. Drizzle with the remaining dressing and toss again to coat. Sprinkle with the crushed chili and serve.
Dressing can made up to 5 days ahead. Store it in the refrigerator and stir to blend if it separates.
The soba noodles may be cooked up to 1 day ahead. Drizzle lightly with oil and store in the refrigerator. Run them briefly under cold water and drain before tossing with the dressing.