Prepare the broccoli. Bring a large pot of water to a boil and preheat the oven to 400°F. Once the water reaches a boil, turn off the heat. Add the chopped broccoli florets to the hot water for 2 minutes, then remove and drain.

Prepare the creamy base. In a large mixing bowl, whisk together the cream of chicken soup, sour cream, and black pepper until smooth.

Melt the Velveeta. Place the Velveeta in a microwave-safe bowl and microwave on high for approximately 1 minute, stopping after 30 seconds to stir. Once melted, whisk the cheese into the cream of chicken and sour cream mixture.

Taste the cheese sauce. Before adding the raw egg, taste the cheese sauce to check whether the salt level is to your liking.

Add the egg. Whisk the egg into the cheese sauce until fully combined.

Assemble the casserole. Add the blanched broccoli and cheese sauce to a 9×13-inch baking dish. Mix until the broccoli is evenly coated, then spread the crushed Ritz crackers over the top.

Bake. Bake at 400°F for approximately 30 minutes. Begin checking the Ritz cracker topping around the 20-minute mark, as oven temperatures can vary. The crackers should develop a deep golden color without burning.

Serve. Remove the casserole from the oven and allow it to cool slightly before serving.