Preheat your oven to 350°F (175°C) and lightly spray a 3-quart baking dish with cooking spray or grease it with butter.

In a large pot, bring water to a rolling boil and add the fresh broccoli florets. Boil for about 4 minutes until crisp-tender, then drain and rinse under cold water.

In a medium skillet, melt 1 tablespoon of butter over medium heat. Add chopped mushrooms and onion, cooking for about 4 minutes until softened and fragrant.

Using the same skillet, melt 4 tablespoons of butter and whisk in flour until smooth. Gradually add milk and half-and-half, simmering for 5-7 minutes until thickened. Stir in salt, pepper, and Greek yogurt.

Pour the sauce over the broccoli and mushroom-onion mixture, then add the egg, 1 cup of cheese, and ½ cup of breadcrumbs, combining all ingredients well.

Transfer the mixture to the baking dish and mix remaining breadcrumbs with melted butter and additional cheese. Sprinkle this topping over the casserole.

Cover with foil and bake for 30 minutes. Remove foil and bake an additional 15-20 minutes until the top is golden brown and bubbling.

Allow the casserole to cool for about 10 minutes before serving.