Place chicken in a large pot. Add all remaining ingredients except cauliflower. Gently stir. Bring to a boil.
Meanwhile, if starting with roughly chopped cauliflower, pulse in a blender until reduced to rice-sized pieces, working in batches as needed.
Once boiling, reduce to a simmer. Stirring occasionally, cook for 6 minutes.
Add riced cauliflower. Continue to cook and stir occasionally until veggies have softened and chicken is fully cooked, about 6 more minutes.
Remove and discard bay leaves. Transfer chicken to a large bowl, and shred with two forks.
Return chicken to the pot, and mix well.