WHISK apple cider or juice with apple cider vinegar, Dijon mustard, fresh tarragon and salt in a medium bowl. Set aside.
CUT chicken breasts in half horizontally. Heat a large non-stick frying pan over medium- high. Add 1 tbsp olive oil, then chicken. Cook until chicken is golden and cooked through, about 3 min per side. Transfer chicken to a plate and cover with foil to keep warm. Reduce heat to medium.
ADD ۱ tbsp olive oil and red onion to frying pan. Cook until onion is soft, about 3 min. Stir in 1apple and cider mixture. Simmer, uncovered, until apple is tender, 4 to 5 min. Season with fresh pepper. Remove from heat. Slice chicken into strips. Arrange torn lettuce on a platter. Top with chicken, Camembert and warm apple mixture.