In a large Dutch oven, melt the butter over low heat. Add the carrots, celery, and shallots, then season with a pinch of salt and a few grinds of black pepper. Increase the heat to medium and cook for about 5 minutes, stirring occasionally, until the vegetables begin to soften.
Add the garlic, wild rice, and flour. Stir well to combine and cook for 1–2 minutes, allowing the rice to lightly toast and the flour to cook.
Slowly pour in the chicken stock, stirring constantly to prevent the flour from clumping. Add the herbs and bring the soup to a gentle simmer. Cover and cook for 40–45 minutes, or until the rice is nearly tender.
Stir in the shredded chicken and heavy cream. Continue simmering uncovered for another 5–10 minutes, until the chicken is heated through and the rice is completely tender.
Taste and season with additional salt and pepper as needed. Serve warm.
