Heat the base — Warm olive oil or butter in a large pot over medium heat until it shimmers slightly.
Soften vegetables — Add onion, carrots, and celery; cook until softened and slightly glossy, about 5–7 minutes, stirring occasionally. You should hear a gentle sizzle and smell sweetness developing.
Add garlic and herbs — Stir in garlic, thyme, rosemary, and bay leaves; cook for 30–60 seconds until fragrant but not browned.
Build the soup — Add chicken, wild rice, chicken broth, and water. Bring to a gentle boil—look for steady bubbles, not a rolling boil.
Simmer gently — Reduce heat to low, cover loosely, and simmer for 35–45 minutes. The rice should open slightly and the chicken should feel tender when pressed.
Remove and shred — Take out the chicken, shred it with forks while warm, then return it to the pot.
Finish with cream — Stir in the heavy cream and let it warm through without boiling; the soup should look slightly thicker and creamy.
Season and rest — Add salt and pepper to taste, then let the soup sit for 5–10 minutes—it thickens naturally as it rests.