Put the chicken in a large bowl. Add the lemon juice and zest, and 1/4 cup olive oil. Season with salt and pepper and toss to combine. Cover and put the chicken in the refrigerator to marinate for 1-2 hours. Remove the chicken from the refrigerator and set aside.
Combine the honey and vinegar in a small bowl and whisk to combine. Stir in the garlic and thyme. Slowly add the olive oil, whisking until combined. Season with salt and pepper. Set aside.
Prepare the chicken. Heat the remaining 2 tablespoons olive oil in a large skillet over medium-high heat. Add the chicken and cook for 6-8 minutes. Turn the chicken over and cook for approximately 8-9 minutes; make sure the chicken is cooked through. Remove from the heat and set aside.
Place the mixed greens in a large bowl. Add the satsuma mandarin oranges, sun-dried tomatoes, and gently mix to combine. Toss with the vinaigrette, reserving a little of the vinaigrette for serving.
Divide the salad on individual plates. Place the chicken on top and drizzle with the reserved vinaigrette. Sprinkle the Parmigiano-Reggiano over the top, if desired. Serve immediately.