Preheat oven to 475°F (246°C). Use 1 tablespoon of butter to grease the bottom of your roasting pan. Slice sourdough bread into 1" cubes and spread them evenly in the bottom of the pan.
Combine the lemon thyme butter ingredients into a bowl and mix until well combined. Loosen the skin of the chicken and rub the lemon thyme butter under the skin. Place the chicken pieces over the cubed sourdough bread.
Bake for 45-50 minutes or until the internal temperature is 165°F (74°C). Remove from the oven and place the chicken pieces on a serving platter to rest. Use a spatula to loosen the bread from the pan and toss in the juices.
Combine the dressing ingredients in a small bowl and whisk to emulsify the oil and vinegar. Toss the dressing, bread cubes, green onions and arugula in a large mixing bowl. Serve on the side with the roasted chicken thighs.