Add the chicken, lemon juice, saffron, and 3 tablespoons of the olive oil to a medium bowl. Season with salt and pepper and toss to combine. Put the chicken in the refrigerator to marinate overnight. Remove the chicken from the refrigerator.
Peel the eggs, slice them in half, and remove the cooked yolk. Place the yolk in a small bowl and set aside. Chop the egg whites. Set aside.
In a medium bowl, combine the parsley, garlic, honey, and vinegar. Slowly add the 1/4 cup of olive oil. Season with salt and pepper and whisk to combine. Add the egg whites and stir until combined. Set aside.
Prepare a grill to medium-high heat. Put the chicken on the grill and cook for approximately 6 minutes, or until they are cooked through. Remove from the grill.
Put the arugula in a medium bowl. Add the egg yolks and toss.
Transfer the arugula to a platter or individual plates. Place the chicken on top of the arugula. Spoon the dressing over the top and sides of the chicken. Garnish with additional parsley and sprinkle with a little black pepper. Serve immediately.