Rinse the wild rice under cold water. Place it in a medium saucepan with the chicken broth and bring to a boil. Reduce heat, cover, and simmer for 40 minutes until the rice is tender and most liquid is absorbed.

While the rice cooks, heat the olive oil in a large skillet over medium heat. Add the chicken breasts and cook 6 to 7 minutes per side until fully cooked through. Remove the chicken, let it rest a few minutes, then shred or cut it into bite-size pieces.

In the same skillet, add the onion, carrots, celery, and mushrooms. Cook 5 to 6 minutes until the vegetables soften. Stir in the thyme, salt, and pepper.

Pour the heavy cream into the skillet with the vegetables and stir to combine. Add the cooked wild rice and shredded chicken. Mix everything until evenly coated and heated through.

Transfer the mixture to a greased 8x8 or similar baking dish. Sprinkle the shredded cheddar cheese evenly over the top.

In a small bowl, toss the breadcrumbs with the melted butter. Scatter this mixture over the cheese layer.

Bake at 375 degrees F for 20 to 25 minutes until the top is golden and the edges are bubbling.