Preheat the oven to 350 degrees F. Soak the red onion, carrots and radishes in ice water for 5 minutes, then drain. Split each roll in half lengthwise to make 4 pieces. Transfer to the oven to toast.
Whisk 1/4 cup mayonnaise, the lime juice, honey, cornichons and brine, and 1/2 teaspoon salt in a large bowl. Add the chicken, onion, carrots, radishes and chopped cilantro and toss. Mix the chile sauce and the remaining 1/4 cup mayonnaise in a small bowl.
Spread each piece of bread with some chile mayonnaise, then top with the chicken salad and cilantro leaves.