Heat oil in a large skillet or frying pan over medium heat. Add bread and season with salt and pepper. Toss to coat and stir until toasted, about 8 to 10 minutes.
Meanwhile, squeeze garlic out of skin into a large bowl. Mash with a fork; whisk in Dijon, lemon juice and oil. Season with salt and pepper and add vegetables, cutting up any larger pieces with a pair of kitchen shears. Add chicken, arugula and bread; toss to combine.
Serve salad topped with goat cheese, a drizzle of pesto and basil.