In a medium bowl, whisk together 6 tablespoons of the olive oil, apple cider vinegar, honey, Dijon mustard, kosher salt, and black pepper until smooth and emulsified.
Transfer half of the mixture to a small bowl, cover, and refrigerate. (This will be the salad dressing.)
Pour the remaining half of the mixture into a zip-top bag. Add the chicken and massage to coat. Seal and refrigerate for at least 30 minutes, or up to 2 hours.
While the chicken marinates, prepare the salad. Trim the tough ends from the Brussels sprouts. Rinse and pat completely dry. Thinly slice the sprouts using a mandoline or sharp knife. Transfer them to a large mixing bowl.
Add the red onion, dried cranberries, Parmesan, sunflower seeds, and the reserved dressing. Toss until evenly coated.
Let the salad rest at room temperature while the chicken cooks so the flavors blend and the Brussels sprouts soften slightly.
Heat the remaining 1 tablespoon of olive oil in a large skillet over medium heat. Remove the chicken from the marinade and discard the marinade. Cook chicken 5-6 minutes per side, until golden brown and cooked through to an internal temperature of 165°F.
Transfer chicken to a cutting board, let it rest 5 minutes, then slice. Place sliced chicken on top of the salad and serve immediately.