Combine the eggs, cream of chicken or mushroom soup (whichever is available), mayonnaise, shredded chicken or turkey, cheese, black pepper, and salt in a large bowl.
Mix everything properly until combined.
Make sure the marinade coats the shredded chicken evenly.
Steam a pack of frozen broccoli for at least 10 minutes until tender.
Grease the baking dish with olive oil.
Spread half of the package of steamed broccoli into the baking casserole. Then, scoop half of the creamy mixture over the top. Spread it fairly to fill the dish.
Layer the rest of the pack of broccoli over the top and pour the remaining creamy chicken mixture over it to form two layers.
Heat the oven to 375° degrees.
Bake the dish for 35-40 minutes until it becomes golden brown and the cheese is all bubbly and melted.