Preheat oven to 375degrees F. Coat a 9-inch deep-dish pie plate with non-stick cooking spray.
Add vegetable oil to a12-inch skillet and place over MEDIUM heat. Add diced onion. Sauté, stirring occasionally for about 3 minutes or until softened. Add ham and garlic to the skillet with the onions and cook, stirring, for just another minute or two or until ham is warmed through and garlic is fragrant. Spoon mixture into the prepared pie dish and spread out evenly.
In a large mixing bowl, whisk together eggs, milk (or cream), ½ teaspoon salt, ½ teaspoon pepper ,and flour. Pour egg mixture over the ham and onions in the pie plate. Sprinkle with Gruyere, cheddar, and chives.
Bake 30 to 40 minutes, until golden brown and completely set in the center. Cool slightly before cutting into wedges.