Preheat oven to 425 degrees. Line a baking sheet with foil.
Toss the veggies (carrots, sweet potato, and squash) in olive oil and sprinkle with salt and pepper (about 1/4-1/2 teaspoon salt and a few grinds of pepper). Roast on the prepared baking sheet for 15 minutes. Add in the quartered onion and garlic and continue to roast for 10-15 minutes.
Meanwhile, shred the chicken. (or you can cook raw chicken breasts in the chicken broth if you are not using rotisserie chicken).
In a large stockpot, bring broth to a simmer. Add the shredded chicken, herbs and remaining salt and pepper.
Once veggies are done roasting, add half to the soup and place the other half in a blender with the 1 cup of water. Make sure to place all onion and garlic in the bender. Puree half of the veggies. Add this puree to the soup and simmer for 5-10 minutes. Add spinach for the last 2 minutes. Adjust seasonings to your taste.