Preheat oven to 250 degrees F (warm oven).
Season chicken thigh pieces with salt and pepper.
Heat olive oil in large sauté, pan over medium-high heat. Add shallots to pan and sauté for 1 minute. Add chicken pieces and radish halves to pan and continue to sauté, until golden brown and cooked through, about 15 minutes.
Remove chicken and radishes to an oven-safe plate and keep warm in oven.
Add broth to sauté pan and turn heat to high. Stir, scraping up any browned bits. Whisk in the Dijon mustard. Reduce heat to medium-low and whisk in the half-and-half. Cook 2-3 minutes more, allowing the sauce to thicken slightly. Remove from heat. Adjust seasoning, if necessary.
Place one serving of watercress on each plate. Divide chicken and radishes among the plates, placing it on top of the watercress, and spoon some of the pan sauce over each serving. Sprinkle sliced scallions on top of each dish.