Preheat oven 325°FSpray baking dish with nonstick cooking spray. Steam the broccoli. Fill the saucepan with about 2 inches of water. Place chopped broccoli into a steamer basket. Cover and steam until tender-crisp (10-15 minutes). Drain. Chop broccoli into smaller pieces if desired, or leave as is.
In the saucepan, melt the butter on medium-low heat. Whisk in flour, salt, and pepper then the milk until smooth. Add cheese and stir constantly until the cheese is melted and smooth. Turn off the heat. Stir in the broccoli and eggs.
Pour mixture into the baking dish. Top with crushed crackers and melted butter.
Bake 30 minutes or until the top is golden and cheese is bubbly. Let cool slightly then serve.
Store leftovers in an airtight container in the refrigerator for 4-5 days. Reheat in the microwave or oven.