Add the wild rice to a medium saucepan with 5 cups of the chicken broth. Bring to a boil over medium-high heat, then reduce the heat to low and cover the pan. Cook until the rice has just started to break open and is slightly tender, 35 to 40 minutes. Set aside.
Meanwhile, bring a pot of water to a boil and prepare an ice water bath. Blanch the broccoli by throwing the florets into the boiling water until bright green and still slightly crisp, 1 1/2 to 2 minutes. Immediately drain the broccoli and plunge it into the bowl of ice water to stop the cooking process. Remove it from the ice water and set aside.
Heat a large pot over medium-high heat, then melt 6 tablespoons of the butter. Add the mushrooms and onions and cook, stirring occasionally, until the liquid begins to evaporate, 3 to 4 minutes. Add the carrots and celery and cook until the vegetables are soft and the mixture begins to turn darker in color, 3 to 4 minutes.
Sprinkle the flour on the vegetables, stir to incorporate it and cook for about a minute. Pour in the remaining 3 cups of broth and stir to combine. Bring the mixture to a gentle boil and allow it to thicken, about 3 minutes. Pour in the heavy cream, stirring to combine. Let the mixture cook until it thickens. Add the salt and pepper, then taste and adjust the seasonings as needed.
Preheat the oven to 375 degrees F.
Mix together the cooked rice and broccoli and tip into a 2-quart baking dish. Using a ladle, scoop out the vegetable/broth mixture and spoon it evenly all over the top, totally covering the surface with the vegetables.
Melt the remaining 2 tablespoons butter, then pour it into a separate bowl with the panko breadcrumbs. Toss the mixture together to coat the breadcrumbs in butter, then sprinkle the breadcrumbs all over the top of the casserole.
Cover with foil and bake the casserole for 20 minutes, then remove the foil and continue baking until golden brown on top, another 15 minutes. Sprinkle on the parsley after you remove it from the oven.