In a bowl, combine ham, green onion, and 2 cups of the cheese.
Use a 1/3 cup of the ham mixture to roll up inside each tortillas and place in the prepared 9 x 13 pan.
in another bowl, whisk together the flour, half and half, and eggs. Pour mixture over the wrapped enchiladas. Cover and refrigerate overnight.
In the morning, preheat oven to 350 degrees and bake covered for 30-40 minutes. Remove foil and sprinkle with the remaining 1/2 cup shredded cheese and cook for 10 more minutes until cheese is melted and eggs are set. Serves 5.