Preheat the oven to 350°F. In a medium pot, combine 1 cup of wild rice blend with 2 cups of low-sodium chicken broth and a pinch of salt. Bring to a boil, reduce heat to low, cover, and simmer for 25 minutes, or until tender. Remove from heat and let the rice sit, covered, for 10 minutes, then drain any remaining liquid and set aside.
Meanwhile, melt 4 tablespoons of butter in a large skillet over medium heat. Add the onion, celery, and carrots. Cook for 5 to 10 minutes, or until softened. Add the minced garlic cloves and cook for 30 seconds, or until fragrant.
Stir in 2 cups of sliced cremini mushrooms, 1 teaspoon smoked paprika, 1 teaspoon Italian seasoning, ½ teaspoon black pepper, and ½ teaspoon salt. Cook for about 4 minutes, or until the mushrooms begin to soften.
Sprinkle 3 tablespoons all-purpose flour over the vegetables and mushrooms and stir constantly for 1 minute.
Slowly whisk in the remaining 1 cup of chicken broth, then whisk in 1 cup of heavy cream and 1 cup of sour cream Simmer gently, whisking often, for about 5 minutes, or until the sauce thickens. Do not boil.
Remove from heat and stir in 1 cup of freshly shredded sharp cheddar cheese and all ½ cup grated Parmesan cheese until melted and smooth.
Stir in 3 cups cooked and shredded chicken and the cooked wild rice until evenly combined.
Transfer the mixture to a greased 9x13-inch (about 3-quart) casserole dish. Tent with foil and bake for 30 minutes, or until hot and bubbling around the edges.
Melt the remaining 2 tablespoons butter and mix with 1 cup panko until evenly moistened. Remove the casserole from the oven, discard the foil, sprinkle the remaining 1 cup cheddar over the top, then add the buttery panko in an even layer.
Return to the oven and bake uncovered for 15 to 20 minutes, or until bubbly and the topping is golden and crisp. Let rest for 5 to 10 minutes before serving.