Cut the ham into small pieces. Add the ham, one cup of cheese, and green onions to a medium-sized bowl and stir well.
Add the ingredients for the egg mixture into a medium-sized bowl and whisk well.
Grease a 9x13 baking dish with non-stick spray. Fill each tortilla with the ham mixture, then roll it up and place it, seam side down, into the bottom of the baking dish. Repeat with all of the tortillas and filling.
Pour the egg mixture over the top and cover the baking dish with plastic wrap. Place in the refrigerator for at least 6 hours, so the tortillas can absorb the egg mixture.
Preheat the oven to 350℉. Remove the plastic wrap, then cover the baking dish with aluminum foil and bake for 38 minutes. Remove the aluminum foil and sprinkle the remaining 3/4 cup of cheese on top. Bake for an additional 15-20 minutes, uncovered, until the cheese is melted and bubbly. Serve with your favorite toppings like sour cream, chopped tomatoes, cilantro, and green onions. Enjoy!