Lightly mist a round 2-quart casserole dish with cooking spray. Alternately place the ham and muffins in the dish to make a shingled pattern. Sprinkle the sundried tomatoes, spring onions and 1/3 cup cheddar over the casserole.
In a large bowl, whisk the eggs, egg whites, milk, and mustard; season with salt and pepper. Pour the custard filling over the casserole and sprinkle with the remaining 1/3 cup cheese. Cover the casserole with plastic wrap; refrigerate at least 5 hours and up to overnight.
Preheat the oven to 175°C. Place the casserole on a large rimmed baking sheet; bake until golden around edges and just set, about 1 hour. Let stand 10 minutes before serving.