Cook the 3/4 pound chicken breast until no longer pink (poach, bake, or pan-sear). Let cool slightly, then shred or cut into bite-sized pieces and set aside.
Peel and finely dice the 3 medium carrots and the 2 medium Yukon Gold potatoes. Dice the 2 stalks celery, the 1 medium onion, and the 1/2 cup white mushrooms (pieces or slices). Mince the 1 clove garlic. Finely chop the 1 teaspoon fresh rosemary.
In a soup pot over medium heat, heat enough of the 3 tablespoons olive oil to coat the bottom of the pot; reserve the remaining olive oil for the roux.
Add the diced carrots, potatoes, celery, onion, and mushrooms to the pot. Cook, stirring occasionally, about 6–8 minutes, until the vegetables are crisp-tender.
Add the minced garlic, chopped rosemary, and 1 teaspoon ground sage to the vegetables. Cook 1–2 minutes more, stirring, until fragrant.
Pour in 3 cups of the 4 cups low-sodium chicken broth and add the cooked chicken to the pot. Bring to a simmer over medium heat, then reduce heat and simmer 15–20 minutes, until the vegetables are completely tender.
While the soup is simmering, make the roux: in a small saucepan combine the 3 tablespoons gluten-free flour with the olive oil you reserved (from the total 3 tablespoons) to make a thick paste. Cook over medium heat, stirring constantly, 1–2 minutes.
Gradually stir the remaining 1 cup of chicken broth into the roux saucepan and bring to a simmer, stirring, until the mixture begins to thicken.
Pour the thickened roux into the soup pot. Simmer the soup 5–10 minutes more, stirring occasionally, until it has thickened slightly.
Stir in 1/8 teaspoon salt and 1/8 teaspoon ground black pepper. If the soup is too thick, add additional chicken broth a little at a time to reach your desired consistency.
Peel and cut the 2 medium oranges into slices or segments and serve them on the side with the soup.