How to Make It
Preheat the oven to 350°. In a small bowl, combine the Ginger-Lime Syrup with the vinegar and soy sauce.
In a medium bowl, lightly mash the diced avocado with a fork. Fold in the lime juice and 1 teaspoon of the olive oil. Season the avocado lightly with salt.
In a medium bowl, toss the radishes with 1 teaspoon of the olive oil and season with salt. Refrigerate the radishes.
Season the chicken breasts with salt and white pepper. Spread the sesame seeds in a shallow dish and press the skinned side of the chicken breasts into the sesame seeds to coat.
Set a large, ovenproof skillet over high heat until very hot. Add the remaining 3 tablespoons of olive oil to the skillet and heat until smoking. Add the chicken breasts, sesame-coated side down, and cook over high heat until the sesame seeds are golden brown, about 3 minutes. Turn the chicken breasts. Transfer the skillet to the oven and bake the chicken for about 5 minutes, or until just cooked through.
Dollop the mashed avocado on plates and top with half of the radish slices. Set the chicken breasts on top and garnish with the remaining radish slices and watercress sprigs. Drizzle the ginger dressing on top and serve.