Melt the butter in a large pot over medium heat. Add the onion, carrots, and celery and sauté for 5 minutes, stirring often until softened and glossy.

Add the garlic and sliced mixed mushrooms to the pot. Cook for 4 minutes, stirring until the mushrooms release their moisture and start to brown at the edges.

Whisk the flour into the vegetables and cook for 1-2 minutes. The mixture should smell nutty and look slightly thicker with no dry flour streaks.

Pour in the chicken broth, then add the wild rice blend, chicken breast, dried thyme, and bay leaf. Bring everything to a simmer and stir so the rice is evenly distributed.

Simmer the soup for 40 minutes, stirring occasionally, until the wild rice is tender and the chicken is cooked through. Skim any foam if needed and look for thickening as the rice releases starch.

Remove the chicken from the pot and shred it. Remove the bay leaf and return only the shredded chicken to the soup.

Stir in the heavy cream and return the soup to a gentle simmer for 5 minutes. It should look creamy and smooth, with small bubbles around the edges.

Season with salt and pepper to taste. Taste and adjust until the flavors pop, then turn off the heat.