Preheat the Oven - Set the oven rack to the center position. Preheat to 350ºF (177ºC). Grease a 9x13-inch baking dish with olive oil on the bottom and sides.
Saute the Potatoes - Heat a large pan or cast iron skillet over medium-high heat. Add 2 tablespoons olive oil. Once hot, add in the potatoes. Saute until tender, occasionally stirring, for 10 minutes.
Saute the Mix-ins - Turn the heat down to medium. Add the onions and garlic, and saute for 1 minute. Add the bell peppers and saute for 2 minutes. Add the ham and saute for 1 minute. Turn off the heat and stir in ½ teaspoon salt, black pepper, and green onions.Transfer the mixture to the greased baking dish and spread it into an even layer. Evenly sprinkle half of the cheddar cheese on top.
Add the Egg Base - In a large bowl, whisk together the cornstarch and 1 teaspoon salt. Add half-and-half and eggs, and whisk until thoroughly combined. Pour the egg mixture into the baking dish. Evenly sprinkle the remaining cheese on top.
Bake the Casserole - Bake for 20 minutes. Rotate the pan and continue baking until the center sets and a toothpick inserted comes out clean, about 20 minutes. The internal temperature should be 180 to 190ºF (82 to 88ºC). Cool for 10 minutes before slicing and serving.