Lightly mist a round 2-quart baking dish with cooking spray. Halve each piece of English muffin and arrange it cut-side down in the baking dish in an overlapping shingled pattern. Tuck the ham between the layers. Sprinkle the scallions and 1/2 cup of the Cheddar over top.
Whisk the milk, mustard and eggs until combined in a large bowl; season with salt and pepper. Pour the egg mixture into the baking dish, cover with plastic wrap and refrigerate for at least 5 hours or overnight.
Preheat the oven to 350 degrees F.
Discard the plastic wrap and sprinkle the remaining 1/2 cup cheese over the casserole. Place the dish on a rimmed baking sheet and bake until the eggs are set and the edges are lightly browned, about 1 hour. Let stand 10 minutes before slicing and serving.
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