Preheat oven to 400°F. Line a rimmed baking sheet with nonstick foil. Place crushed cornflakes in a shallow bowl.
Brush chicken breasts with 1/4 cup buttermilk. Season with cayenne, 1/2 tsp salt, and 1/4 tsp pepper. Coat in crushed cornflakes, pressing gently to adhere. Place on the prepared baking sheet.
Bake for 15 to 20 minutes or until cooked through and golden. Let rest slightly, then slice if desired.
In a large bowl, whisk together sour cream, vinegar, Dijon mustard, remaining 1/4 cup buttermilk, and 1/4 tsp each salt and pepper. Stir in tarragon.
Add lettuce and toss to coat. Gently fold in fennel and cucumber.
Plate the salad and top with crispy chicken. Garnish with chopped chives.