How to Make It
Wrap a 10-inch cast-iron skillet in aluminum foil, covering entire base of skillet. Set aside.
Pat chicken thighs dry with paper towels, and sprinkle both sides of thighs evenly with salt and pepper. Heat oil in a 12-inch nonstick skillet over medium-high. Place chicken, skin side down, and lemon slices in skillet. Place prepared cast-iron skillet, bottom side down, on chicken. Cook until skin side is golden brown and crispy, 8 to 10 minutes, checking after 8 minutes. Turn chicken breasts, and place cast-iron skillet, bottom side down, on chicken. Cook until done, about 6 minutes. Remove from skillet, reserving lemon slices and 3 tablespoons of drippings in skillet, and cover chicken to keep warm.
Add haricots verts, carrots, and shallots to nonstick skillet. Cook over medium-high, stirring often, 4 minutes. Add 1/2 cup each of the wine and stock. Cover and reduce heat to medium; cook until haricots verts and carrots are tender, about 8 minutes. Remove vegetables, and cover to keep warm. Set aside lemon slices.
Squeeze juice from lemon slices into skillet; discard lemon slices. Add mustard, honey, and remaining 1/2 cup each wine and stock; stirring and scraping to loosen browned bits from bottom of skillet. Bring mixture to a simmer over medium, stirring occasionally. Cook 1 minute. Add butter, tarragon, thyme, and parsley. Cook, stirring constantly, until butter is melted. Remove from heat.
Place 2 chicken thighs on each of 4 plates. Divide vegetable mixture evenly among plates. Drizzle plates evenly with sauce. Serve with potatoes, rice, or pasta.