Preheat the oven to 300 degrees F. Fry the hash browns and potato wedges in canola oil in separate skillets according to the package directions until golden brown and crisp. Season with salt and pepper. (You can also bake the potatoes in the oven, if you prefer.) Drain on paper towels and keep warm.
Heat 2 tablespoons butter in a large skillet over medium heat. Throw in the veggies and ham; toss around for several minutes, until the onions are just softened. Turn off the heat and allow to stay in the pan.
In 4 individual ovenproof skillets (or one very large one), layer the hash browns, veggie-ham mixture and grated cheese. Place in the oven for a minute or two, until the cheese is melted. Remove from the oven with an oven mitt, as the skillet will be hot.
Melt the remaining 2 tablespoons butter in a nonstick skillet and fry the eggs to the specifications of your guests.
Place 5 potato wedges over the top of the melted cheese, then top with 2 eggs per skillet. Spoon salsa or pico de gallo over the top and serve immediately.