Preheat the oven to 425F convection or 450F regular bake. Line a baking sheet with parchment paper.
Add the beans and carrots to the baking sheet and drizzle with 2 tablespoons olive oil and sprinkle with ½ teaspoon salt and ½ teaspoon pepper. Use your hands to toss to coat well, then spread out evenly on the baking sheet.
Pat the chicken thighs dry, then drizzle the remaining 1 tablespoon oil and sprinkle with remaining ½ teaspoon salt and ½ teaspoon pepper. Rub around to coat, then arrange them evenly spaced out on the baking sheet.
Bake for 25-30 minutes or until the beans have crisped and the chicken has browned.
Meanwhile, in a large bowl, whisk together all of the dressing ingredients until combined. Add the greens and herbs and use your hands to toss to coat well. You can toss the carrots/beans into the salad if your salad greens are on the heartier side (otherwise they can wilt down too much from the heat).
Transfer the chicken to a cutting board and slice/chop it up. Serve the salad topped with the carrots/beans and chicken (or keep them on the side) and sprinkled generously with cheese and nuts.