Cook the broccoli for about 2 minutes in boiling water, just until crisp-tender. Drain and set aside.
Preheat oven to 350°F. Grease an 8-inch square baking dish; set aside.
In a large skillet or Dutch oven, melt butter over medium-high heat. Add onion and celery; cook, stirring occasionally, until the onion is translucent, about 5 minutes. Add garlic; cook until fragrant, about 30 seconds.
Reduce the heat to a very low flame. Stir in soup, paprika, dry mustard, nutmeg, 1 cup of the cheese and milk. Cook, stirring constantly, until the cheese melts, about 2 minutes. Remove from heat.
Add cooked rice and broccoli; stir to combine. Taste and season with salt and pepper, if necessary.
Transfer mixture to the prepared baking dish. Top with crushed crackers and remaining ½ cup of cheese.
Bake for about 20 minutes, or until hot and bubbly.