In a large bowl, combine 1 can (10.75 oz) condensed cream of celery soup, 2 cups grated sharp cheddar cheese, ½ teaspoon salt, and ½ teaspoon pepper. Stir until well combined.
Add 40 ounces frozen broccoli (thawed) and stir until the broccoli is evenly coated with the cheese mixture.
Pour the broccoli mixture into the prepared slow cooker.
Sprinkle 1½ cups crushed Ritz crackers evenly over the top.
Top with the remaining ½ cup grated sharp cheddar cheese.
Cover with the lid and cook on LOW for 5 hours or HIGH for 2½ hours.