Grease 6 1-cup ramekins. In a large bowl, whisk together eggs, mustard and salt. Whisk in milk and half-and- half. Mix in bread, ham, scallions and 1 cup cheese. Pour mixture into prepared dishes. Cover with plastic wrap and refrigerate for at least 6 hours and up to 10 hours.
Preheat oven to 375°F and remove stratas from refrigerator while oven heats. Bake stratas uncovered for 30 minutes, then sprinkle remaining cheese over tops, and bake 10 minutes longer. Let stand 5 minutes before serving.