Preheat the oven to 400°F. Spray a 9x13 inch (or 3 quart) casserole dish with nonstick spray.
Pour the milk into a medium saucepan with the cornstarch and whisk to dissolve it before you turn on the heat. Turn the heat up to medium-high and stir in the butter, chicken bouillon, salt, pepper, onion powder, and garlic powder. Bring the mixture to a boil and stir for 30 seconds to 1 minute until thickened.
Turn the heat down to medium-low and stir in the cream cheese and 1 1/2 cups of shredded cheddar cheese. Stir until the cream cheese is melted into the sauce then remove it from the heat and allow it to cool slightly.
While it’s cooling, bring a large pot of salted water to a boil. Add the broccoli florets and boil for 3 minutes, until the broccoli is noticeably brighter in color. Immediately drain the broccoli in a colander to stop the cooking process. Transfer the broccoli to the prepared casserole dish.
When the creamy sauce is cooled, add the beaten egg. Make sure the mixture isn’t too hot or it could scramble the eggs. To be safe, you could add a bit of the mixture to the eggs first to temper it (bring it up to temp) before adding it to the mixture.
Pour the creamy mixture over the broccoli and toss to coat. Sprinkle the remaining 1 1/4 cups of shredded cheese on top.
Quickly mix the Ritz crackers with butter and garlic. Sprinkle evenly over the broccoli casserole
Bake in the preheated oven for 35-40 minutes, or until the edges are bubbling and the top is golden brown. Serve warm.
Broccoli casserole will stay fresh in an airtight container in the fridge for up to 4 days.