Cook the broccoli for about 2 minutes in boiling water, just until crisp-tender. Drain and set aside.
Preheat the oven to 350°F. Grease a 2-quart baking dish or spray with nonstick cooking spray; set aside.
In a large skillet or Dutch oven, melt the butter over medium-high heat. Add the onion and celery; cook, stirring occasionally, until the onion is translucent, about 5 minutes. Add the garlic; cook until fragrant, about 30 seconds.
Reduce the heat to a very low flame. Stir in the soup, paprika, dry mustard, nutmeg, 1 cup of the cheese, and the milk. Cook, stirring constantly, until the cheese melts, about 2 minutes. Remove from the heat.
Add the cooked rice and broccoli; stir to combine. Taste and season with salt and pepper. This is also a good time to add other herbs and spices if you like, such as thyme, rosemary, parsley, or cayenne.
Transfer the mixture to the prepared baking dish. Top with the remaining ½ cup of cheese and the crackers crumbs.
Bake for about 30 minutes, or until the filling is hot and the topping is golden brown.