Sprinkle chicken with salt and drizzle with 1 tablespoon olive oil. Add chicken to pan, skin side down, and sear until crispy and brown. Remove carrot tops and reserve. Flip chicken over, then add whole carrots to the pan. Top chicken and carrots with cubed butter. Transfer pan to the oven, and bake for 20 minutes.
In a small bowl with a lid, combine lemon juice, garlic, salt, remaining olive oil and honey. Close tightly and shake until combined.
Finely chop carrot tops and toss with the dressing.
Plate chicken and greens, and drizzle leftover pan drippings over top before serving.