Preheat oven to 350°. Spray a 13x9-inch baking dish with nonstick cooking spray.
In a stockpot, bring broccoli, next 3 ingredients, and water to cover to a boil over high heat. Reduce heat, and simmer for 4 minutes or just until crisp-tender. Drain well.
In a large bowl, whisk together soup, sour cream, and egg. Add drained broccoli mixture, 2 cups cheese, and 1 cup crushed crackers. Pour into prepared pan.
In a small bowl, stir together butter, remaining 1½ cups crackers, and remaining ½ cup cheese. Sprinkle over broccoli mixture.
Bake for 30 minutes or until hot and bubbly.
Notes
Casserole can be assembled through step 3, covered, and refrigerated overnight. Let it stand at room temperature for 30 minutes before topping with cracker mixture and baking as directed.
Recipe by Paula Deen Magazine at https://pauladeenmagazine.com/broccoli-cheddar-casserole-recipe/