Heat olive oil in a large stockpot over medium heat. Season chicken breasts with garlic powder, salt and pepper, to taste. Add chicken to the stockpot and cook until golden, about 2-3 minutes; set aside.
Heat another 2 Tbsp oil in the stockpot over medium heat. Add onion, mushrooms, carrots and celery. Cook, stirring occasionally, until tender, about 5 - 6 minutes. Stir in minced garlic, thyme until fragrant, about 1 minute.
In a large bowl, whisk in arrowroot starch with 1/4 cup of the chicken stock until combined, about 1 minute. Add in remaining chicken stock, chicken breasts and arrowroot starch mixture to the stockpot, and cook, stirring constantly, until slightly thickened, about 4-5 minutes.
Stir in half and half until heated through, about 1-2 minutes; season with salt and pepper, to taste. If the soup is too thick, add more half and half as needed until desired consistency is reached.
Serve immediately, garnished with fresh rosemary, if desired.