Pre-heat the oven to 400°F.
Combine the walnuts with the soft cheese, spinach, garlic, salt, pepper and nutmeg. Season the chicken with salt and pepper and divide the cheese mixture among the breasts. Close the chicken breasts over the filling. Wrap the chicken with bacon or speck, slightly overlapping the slices.
Heat a heavy skillet over medium-high heat with 1 tablespoon oil and lightly brown the chicken on all sides. Transfer the skillet to the oven and bake for 15-20 minutes to cook through.
While the chicken is in the oven, whisk up the lemon juice, vinegar, Dijon, honey and the remaining olive oil. Combine the apple, celery, onion and greens with dressing and season with salt and pepper.
Serve the stuffed chicken with the salad alongside.