Rinse 1 cup (190g) of wild rice under cold running water. Add to a saucepan with 2.5 cups (600ml) water and a pinch of salt. Bring to a boil, reduce to low, cover, and simmer for 45-55 minutes until grains split open and are tender. Drain and set aside.
Place chicken breasts in a pot and cover with water or broth. Bring to a gentle boil, reduce to a simmer, and cook for 15-18 minutes until fully cooked (165°F/74°C). Remove, rest for 5 minutes, then shred with two forks and set aside.
In a large Dutch oven over medium heat, melt 4 tablespoons (60g) butter. Add the diced onion and sauté for 4-5 minutes until soft and translucent. Add the diced carrots and celery and cook 3-4 minutes until softening. Add the garlic and sliced mushrooms and cook 3-4 minutes until mushrooms release moisture and begin to brown slightly.
Sprinkle 1/3 cup (42g) of flour evenly over the sautéed vegetables and stir well to coat. Cook the flour mixture for 1 full minute, stirring constantly, until it smells slightly toasty.
Slowly pour in the 6 cups (1.4L) of chicken broth in a thin stream while stirring constantly to prevent lumps. Add the dried thyme, crumbled rosemary, bay leaves, garlic powder, onion powder, and a generous pinch of black pepper. Bring to a gentle simmer, reduce heat to medium-low, cover, and cook for 40 minutes, stirring every 5-7 minutes.
Remove and discard the bay leaves. Add the shredded chicken and cooked wild rice to the pot and stir to combine. Slowly pour in 2 cups (480ml) of half-and-half while stirring. Keep the heat at a low simmer and cook for an additional 5-10 minutes, uncovered, until the soup reaches your desired consistency.
Taste and adjust seasoning with salt, pepper, or additional herbs. Stir in a squeeze of fresh lemon juice for brightness, if desired. Ladle into bowls, garnish with fresh chopped parsley, and serve hot with crusty bread or crackers.