Parboil potatoes. Cut the potatoes into small cubes. Add the potatoes to a large pot of cold salted water. Turn heat to high and cook for 10 minutes beginning from the time you started the heat. Once the 10 minutes have passed, strain the potatoes. They should be slightly soft but not cooked through. Set them aside.
Crisp the ham. In a large cast-iron skillet, heat a ½ tablespoon of olive oil over medium heat. Once hot, add the diced ham. Occasionally stir to get the ham crispy, 6 to 8 minutes. Remove the ham and set it aside while leaving the drippings in the pan.
Crisp the potatoes. Into the still hot cast iron pan, add another ½ tablespoon of olive oil and the par-cooked potatoes over medium heat. Stir the potatoes every few minutes to allow them to crisp on all sides. This should take about 20 minutes. Once browned and cooked, remove them and set them aside.
Sauté vegetables. Add ½ a tablespoon of olive oil to the hot cast iron pan. Then add the diced onion, bell pepper, and mushrooms and sauté for 7 to 9 minutes or until soft.
Add jalapeño and garlic. Make a space in the middle of the pan and add the jalapeño and garlic and sauté for 2 minutes before mixing them throughout the rest of the pan.
Cook eggs. Cook the eggs to your preference. If you don't want them scrambled, begin cooking them in a separate pan while sautéing the veggies. I made a space in the center of the pan and then added the eggs before mixing them throughout the ingredients. This scrambled the eggs amongst the food.
Add remaining ingredients. Add the ham and potatoes into the cast iron skillet and stir for 2 minutes. If you cooked your eggs separately, place them atop the hash. Serve hot with toasty bread.