Heat oven to 425(F) degrees. Press hash browns into 9x13 baking dish and drizzle melted butter over top. Bake for 25 minutes. Remove from oven and lower temp to 350(F) degrees.
Meanwhile, mix eggs, whole milk, dry mustard and black pepper.
Layer onion, ham, broccoli and cheese over hash browns and then gently pour egg and milk mixture over top. Press contents down evenly. Bake for 50 minutes or until a knife inserted comes out clean.
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