Saigon Chicken Salad

INGREDIENTS

• 3 cups 2-inch pieces trimmed Chinese long beans or green beans (about 10 ounces)
• 1 cup coarsely grated carrot
• 1/2 cup olive oil
• 1 cup celery leaves
• 1 cup very thinly sliced green cabbage
• 3 green onions, thinly sliced on diagonal
• 1/4 cup (packed) light palm sugar or golden brown sugar
• 1/4 cup fresh lime juice
• 1/2 cup salted roasted peanuts, split in half
• 2 teaspoons minced Thai chiles or serrano chiles with seeds
• 1 cup fresh cilantro leaves
• 1 4-inch-long bottom portion of large lemongrass stalk, finely chopped (about 2 tablespoons)
• 1 1/4 pounds skinless boneless chicken breast halves (4 to 5)
• 2 large garlic cloves, pressed
• 8 ounces plum tomatoes, halved lengthwise, seeds and pulp removed, shells cut into long thin strips
• Coarse kosher salt
• 5 tablespoons fresh lemon juice
• 3 large kaffir lime leaves, minced (1 generous teaspoon)
• 1 cup chopped fresh cilantro (including stems)
• 1 cup coarsely grated peeled daikon (Japanese white radish) or trimmed red radishes
• 1 cup coarsely grated seeded Persian cucumbers (about 3)
• 5 tablespoons fish sauce (such as nam pla or nuoc nam)