In a deep pot, add the potatoes and enough water to cover. Bring to a boil, salt the water and cook the potatoes until tender, 15 minutes. Drain.
In a large nonstick skillet, heat the EVOO, 1 turn of the pan, over medium-high heat. Season the chicken with salt and pepper; add to the skillet and cook, turning once, until golden, 12 minutes. Transfer to a plate; cover with foil to keep warm.
In the same skillet, melt the butter over medium heat. Add the apple, pear and nutmeg; season with salt. Stir in the lemon juice for 3 minutes, then stir in the honey for 1 minute.
Mash the potatoes with the milk and cheese; season with salt and pepper. Slice the chicken breasts on an angle, arrange alongside the potatoes and top with the fruit. In a small bowl, combine the chives, thyme and lemon peel; sprinkle over the chicken and potatoes.