Cook the wild rice. Rinse 1 cup of wild rice blend.
In a medium pot, bring 3 cups chicken broth to a boil with a bay leaf. Add the rice, reduce to a simmer, cover, and cook until tender and most liquid is absorbed, about 40–45 minutes. Fluff and discard the bay leaf.
If using pre-cooked rice, you’ll need about 3 cups.
Sauté the veggies. In a large skillet over medium heat, warm 1 tablespoon olive oil. Add onion, celery, and carrots with a pinch of salt. Cook 6–8 minutes until soft.
Add mushrooms and cook until they release moisture and brown slightly, 5–7 minutes. Stir in the garlic for 30 seconds.
Make the creamy base. Push the veggies to the edges. Melt 4 tablespoons butter in the center.
Sprinkle in 1/4 cup flour and whisk into a paste (roux) for 1–2 minutes. Gradually whisk in 1 1/2 cups milk and 1 cup chicken broth until smooth and slightly thickened, 3–5 minutes.
Season it well. Stir in thyme, parsley, 1/2 teaspoon salt, and 1/2 teaspoon pepper. Taste and adjust salt.
Turn off the heat. Stir in Parmesan and optional shredded cheddar/Gruyère until melted. Fold in 1/2 cup sour cream or Greek yogurt.
Add chicken and rice. Fold the shredded chicken and cooked wild rice into the sauce until everything is coated and evenly distributed.
Assemble the casserole. Transfer the mixture to a greased 9x13-inch baking dish.
In a bowl, toss panko (or crushed crackers) with a drizzle of olive oil, a pinch of salt, and a little extra Parmesan if you like. Sprinkle evenly over the top.
Bake. Heat oven to 350°F (175°C). Bake uncovered for 25–30 minutes, until bubbling at the edges and the topping is golden.
If the top needs more color, broil for 1–2 minutes, watching closely.
Rest and serve. Let it sit 5–10 minutes so it sets up. Finish with chopped parsley or chives. Serve warm.