Set the oven rack to the center position. Preheat to 350ºF (177ºC). Grease a 9×13-inch baking dish with olive oil on the bottom and sides.

Heat a large pan or cast iron skillet over medium heat. Add in the sausage and saute until fully cooked and browned, about 3 to 4 minutes. Evenly spread into the baking dish and drain off most of the fat.

Heat the pan over medium-high heat and add 2 tablespoons of olive oil. Once hot, add the potatoes and saute until tender, occasionally stirring, about 8 to 10 minutes.

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. Turn off the heat and stir in ½ teaspoon salt, black pepper, and green onions. Transfer the mixture to the greased baking dish, mix it with the sausage, and spread it into an even layer. Evenly sprinkle half of the cheddar cheese on top.

In a large bowl, whisk together the cornstarch and 1 teaspoon salt. Add the half-and-half and eggs and whisk until thoroughly combined. Pour the egg mixture into the baking dish and evenly sprinkle the remaining cheese on top.

Bake for 20 minutes. Rotate the pan and continue baking until the center sets and a toothpick inserted comes out clean, about 20 minutes. Cool for 10 minutes before slicing and serving.