Finely chop the onion. Slice the mushrooms. Mince the garlic.

Set a large pot over medium-high heat and add the butter. Once melted, add the onions and mushrooms. Saute until the vegetables are browned and softened, 6-7 minutes. Add the minced garlic and continue cooking until fragrant, about 30 seconds.

Sprinkle the flour into the pot and stir to coat the onions and mushrooms. Slowly pour the chicken broth into the pot, stirring to dissolve the flour. When no lumps remain, pour in the half-and-half while continuing to stir.

Cook the sauce, stirring constantly, until it begins to bubble and thicken. Once thickened, turn off the heat. Stir in the sour cream, shredded cheese, salt, and black pepper. Once the cheese is mostly melted, fold in the rice, chicken, and broccoli until thoroughly coated in sauce.

Pour the chicken, rice, and broccoli mixture into the prepared baking dish.

Place the cracker crumbs, garlic powder, and shredded cheese in a mixing bowl. Pour in the melted butter. Mix with a fork until the crumbs are evenly moistened.

Sprinkle the crumbs in an even layer over the casserole.

Bake the casserole on middle rack of oven until topping is deeply golden and the dish bubbles at the edges, 35-40 minutes.

Check to see that casserole is done. Remove from oven or add time as needed.

Allow the casserole to rest for 10-15 minutes before serving.