Preheat your oven to 350 degrees. Lightly grease a 13-by-9-inch baking dish with nonstick cooking spray.
Add the butter and olive oil to a medium skillet over medium-high heat. Thinly slice the scallions, keeping the whites and greens separate. Place the greens in a small bowl and set the bowl aside.
Add the scallion whites and garlic to the skillet and cook, frequently stirring until the contents are fragrant, about 30 seconds. Set the contents aside in a small bowl to cool.
Chop the broccoli head into bite-sized florets. Pour the water and kosher salt into a large saucepan; bring the water to a boil, and then add the broccoli. Cover the saucepan and steam the broccoli for 3 minutes or until the broccoli is crisp-tender. Drain the saucepan and set it aside to cool.
In a large bowl, beat the eggs with a whisk until the yolks and whites are thoroughly combined. Add the garlic and onion mixture, the steamed broccoli, the chopped ham, and the cottage cheese, flour, and shredded cheese. Season the mixture with salt and pepper and whisk until blended.
Pour the mixture into the prepared baking dish. Bake for 35-40 minutes or until the eggs are set and thoroughly cooked. Garnish the casserole with scallion greens and serve it immediately. Enjoy!