Prep this the night before and cook in the morning.
Stir together ham, green onions and 2 cups of cheese. Use a 1/3-cup measuring cup to scoop out cheese mixture onto a tortilla. Roll up tortilla and place seam side down in a 9 x 13 inch baking dish. Roll up all tortillas and squeeze them into the baking dish.
Whisk together half-and-half, eggs and flour. Pour over tortillas. Cover and let sit overnight.
In the morning, preheat oven to 350ºF. Bake for 30-40 minutes. Remove and sprinkle remaining 1/2 cup of cheese over enchiladas. Bake for 10 more minutes.
Serve with salsa.