Heat a grill to medium-high heat. Rub the chicken with 1 tablespoon of olive oil then season all over with salt and pepper. In a small bowl stir together the thyme, oregano, rosemary and parsley then sprinkle it liberally to evenly coat the chicken.
Preheat grill to high, making sure that the grill grates are clean and free from food debris. Grill until completely cooked through, about 6 minutes each side. Remove and let stand for about 10 minutes then slice against the grain and set aside.
Heat oven to 400ºF (200ºC).
Toss the vegetables in the remaining olive oil and spread in an even single layer on an aluminum foil-lined baking sheet. Season with salt and pepper then roast until tender and slightly golden-brown, about 20 minutes.
Add the salad mix to a large mixing bowl along with the vegetables and toss with the lemon vinaigrette. Top with the Asiago cheese, croutons and chicken. Divide into salad bowls to serve.