Preheat oven to 400.

Season chicken, cut small slice from apple; finely chop to make 1 tbs minced. Put minced apple in small bowl, add shallot, whisk in 2 tbs cider vinegar and mustard. Let sit for 10 min. Whisk in 2 tbs oil; season.

Heat 1-2 tbs oil in large ovenproof skillet over med-high heat. Add chicken and cook till golden brown about 4 min. Flip chicken and transfer skillet to oven. Roast till cooked through, 12-14 min. Tranfser to plate; set aside. Reserve skillet.

Return skillet to med-high heat. Add cider, scrape browned bits; boil till liquid reduced by half, 2-3 min. Add remaining 1 tbs vinegar. Remove pan from heat and swirl in butter. Season.

Thinly slice remaining apple and transfer to med bowl. Add lettuces and fennel. drizzle some vinaigrette over, season and toss. divide salad and chicken among plates; spoon sauce over chicken.