Pat the chicken pieces dry and season with 1/2 teaspoon of the salt and the pepper. Heat the olive oil in the large pot over medium-high heat. Add the chicken in a single layer and sear 2–3 minutes per side until golden. The chicken does not need to be fully cooked yet — transfer it to a plate.

Reduce the heat to medium. Add the onion, carrots, celery, and mushrooms to the pot with the remaining 1/2 teaspoon salt. Cook, stirring, until the vegetables soften and the mushrooms release their liquid and start to brown, about 5 minutes. Stir in the garlic, thyme, and dried parsley; cook 1 minute more, until fragrant.

Stir in the quick-cooking wild rice blend. Pour in the chicken broth and add the bay leaf, scraping up any browned bits from the bottom of the pot. Bring to a lively simmer.

Reduce the heat to medium-low and simmer, partially covered, until the rice is tender and the chicken is cooked through, about 12 minutes. Return the seared chicken (plus any juices from the plate) to the pot for the last 5 minutes of simmering.

In a small saucepan over medium heat, melt the butter. Whisk in the flour and cook 1–2 minutes, until it smells toasty. Slowly whisk in the milk until smooth, then the heavy cream. Simmer 1–2 minutes until lightly thickened.

Remove the soup from the heat. Slowly stir the cream base into the pot. Adding cream off the heat keeps the soup silky instead of split or grainy. Remove the bay leaf, taste and adjust the salt, shower with fresh parsley, and serve.