Preheat oven to 400 degrees. Grease a deep 12to 2-quart baking dish. Set aside 2 cup of the cheese for the top. Place 1/3 of the cheese on the bottom of the baking dish. Add 1/3 of the crab and 1/3 of the chilies. Repeat, making 3 layers of each. Whisk the half-and-half with the eggs and flour, and slowly pour into the baking dish. Top with the marinara sauce and sprinkle with the reserved cheese. Bake, uncovered, for 1 hour, or until hot and set in center.