Cold Soba-Noodle Salad with Chicken, Peppers, and Cucumber

INGREDIENTS

• Coarse salt and ground pepper
• 8 ounces soba (Japanese buckwheat noodles)
• 2 tablespoons vegetable oil, such as safflower
• 1 teaspoon toasted sesame oil
• 2 tablespoons fresh lime juice, plus lime wedges, for serving
• 2 tablespoons rice vinegar
• 2 bell peppers (ribs and seeds removed), thinly sliced
• 1 cup torn fresh basil leaves
• 1 English cucumber, peeled, halved lengthwise, seeded, and thinly sliced
• 1 rotisserie chicken, skin and bones removed, meat shredded (about 4 cups)