Heat the olive oil in a large Dutch oven or soup pot over medium heat. Add the onion and carrots and sauté until softened, about 5–7 minutes. Remove the vegetables from the pot and set aside.
2 large carrots, 1 onion, 2 tablespoons olive oil
Add the half-and-half and bone broth to the pot and warm over medium heat, stirring frequently.
2 cups half and half, 2 cups bone broth
Whisk together the tapioca starch and cold water to make a slurry. Then whisk the slurry into the warm broth mixture until it's smooth and there are no clumps.
2 tablespoons tapioca starch, 2 tablespoons cold water
Return the sautéed vegetables to the pot, and add the chicken breasts and broccoli. Bring to a gentle simmer, then cover and cook for 30–40 minutes, or until the chicken is cooked through and the broccoli is tender.
2 chicken breasts, 12 ounces broccoli
Remove the chicken from the pot and shred with two forks. Then return the shredded chicken to the soup.
Slowly stir in the cheese until melted and creamy, and season the soup with salt and pepper. Enjoy warm!
2 cups cheddar cheese, 1 teaspoon salt, 1/4 teaspoon pepper