First, prep the chicken. In a large bowl, combine the olive oil, balsamic, lemon juice, Dijon mustard, garlic powder, salt, and pepper. Whisk until smooth. Add the chicken breasts, turning once to coat in the marinade. Cover bowl and transfer to the fridge for at least 20 minutes and up to 4 hours.
When ready to cook, discard marinade and grill the chicken to an internal temperature of 165 degrees F. Set chicken aside and slice when slightly cooled.
To make the dressing, combine all dressing ingredients in a small jar with a tight-fitting lid. Cover, shake well, and set aside until ready to serve. Dressing can be stored in the fridge for as much as 1 week.
To assemble the salads, lay lettuce out on a platter or individual salad plates. Top with bacon, eggs, tomatoes, carrots, avocado, onion, and sliced chicken, laying ingredients out in rows for a traditional Cobb salad look. Sprinkle on cheese and drizzle on dressing, if desired, or serve with those on the side.