Pour 3 tablespoons of the oil in a skillet and heat to medium. Add the hash browns and leave them undisturbed for a few minutes. Make sure the skillet's not too hot. Ideally you'll turn them only once and then cook them on the other side--you want them crispy and golden. Sprinkle with salt and pepper.
In another skillet, add about an inch of oil. Heat over medium heat until a deep-fry thermometer inserted in the oil registers 350 degrees F. Fry the potato wedges until golden brown and crisp. Sprinkle with salt and pepper. (You can also bake these in the oven if you prefer.) Drain the hash browns and potato wedges on a paper towel and keep warm.
Heat 2 tablespoons of the butter in a large skillet until melted. Throw in the ham, jalapenos if using, onions and bell peppers and toss them around for several seconds. Turn off the heat and set the pan aside.
In 8 individual skillets (or 1 very large one) layer: the hash browns, the veggie/ ham mixture and then the grated cheese. Bake for a minute or 2, until the cheese is melted. Remove from the oven with an oven mitt, as the skillets will be hot.
Melt 1 tablespoon of the butter in a nonstick skillet and fry the first 4 eggs, then remove and set aside. Add the remaining tablespoon of butter and fry the remaining 4 eggs.
Place the potato wedges over the top of the melted cheese, then top with 1 egg per skillet. Spoon the salsa over the top and serve immediately. Enjoy!