Preheat oven to 375F
Heat a large cast iron skillet over medium heat. Add in the avocado oil and once the oil is hot add in the diced potatoes. Turn down the heat to low/medium heat and cover. Cook for 10-12 minutes stirring a couple of times during that time.
While the potatoes are cooking mix up your sourdough batter. In a large bowl add in the sourdough starter, eggs, baking soda, butter, salt, and oregano. Whisk together until combined and set aside.
Once the potatoes are tender and lightly golden brown add in the ham and green beans. Stir in the onion, garlic, and mustard powder. Salt and pepper to taste and then add in the flour. Stir for about a minute to evenly coat the filling. Pour in the half and half and stir until thick. Remove from heat.
Pour the sourdough batter over the top of the filling and place in your preheated oven. Bake for 20 minutes or until the topping is cooked through. Remove from oven and sprinkle the cheese over the top. Place the pan back in the oven and bake for an additional 5 minutes. Once the cheese is all gooey and melted remove from oven and let it rest for 10 minutes before serving.