Cook the wild rice: Prepare the wild rice blend according to the package directions. Measure 1 1/2 cups of uncooked rice before cooking, or prepare enough to yield the required amount of cooked rice.
Prepare the oven: Preheat the oven to 350°F. Lightly coat a 9×13-inch baking dish with nonstick cooking spray.
Season the chicken: Pat the chicken pieces dry with paper towels. Toss them with salt, pepper, and paprika.
Sear the chicken: Heat 2 tablespoons of olive oil in a large Dutch oven over medium-high heat. Add the chicken in a single layer and sear for about 1 minute without moving it. Continue cooking and stirring until the chicken is opaque but not fully cooked. Transfer it to a large bowl with a slotted spoon.
Cook the vegetables: Add a little more olive oil or butter to the pot if needed. Add the onion, carrots, and celery. Sauté until the onion becomes tender. Add the garlic and cook for about 30 seconds. Transfer the vegetables to the bowl with the chicken.
Brown the mushrooms: Melt 2 tablespoons butter with a small drizzle of olive oil over medium-high heat. Add the mushrooms and stir to coat. Arrange them in a single layer and cook until deeply golden on both sides. Transfer them to the chicken and vegetable mixture.
Make the sauce: Whisk the chicken broth and cornstarch together in a bowl or liquid measuring cup. Set aside. Without wiping out the Dutch oven, melt 2 tablespoons butter with 1 tablespoon olive oil over medium heat.
Whisk in the flour and cook for 2 minutes, stirring constantly. Reduce the heat to low and gradually whisk in the broth mixture and milk.
Add the Dijon mustard, Worcestershire sauce, chicken bouillon, parsley, basil, thyme, salt, and pepper. Bring the sauce to a gentle simmer, whisking frequently, until thickened.
Remove the sauce from the heat. Whisk in 1 cup cheddar cheese until melted, then add the Parmesan and stir until smooth.
Combine the casserole: Add the cooked chicken, vegetables, mushrooms, and wild rice to the sauce. Stir until evenly combined. Taste and adjust the salt and pepper as needed.
Transfer the mixture to the prepared baking dish. Sprinkle the remaining 1 cup cheddar cheese evenly over the top.
Make the topping: Melt the butter and olive oil in a medium skillet over medium heat. Add the panko breadcrumbs and stir until coated. Cook until the crumbs are golden brown, then sprinkle them evenly over the cheese.
Bake: Cover the dish and bake for 30–35 minutes, or until the casserole is hot and bubbling and the cheese has melted. Let it rest for about 5–10 minutes before serving.