Cook the bacon over medium-high heat in a 12-inch nonstick skillet, stirring occasionally, until crisp, 10 to 12 minutes. Remove the bacon using a slotted spoon and drain on paper towels.
Add the potatoes, 1 teaspoon salt and 1/4 teaspoon pepper to the pan juices. Cook, stirring frequently, until brown and crisp, about 25 minutes. Remove the potatoes using a slotted spoon and drain on paper towels. Add the oil, onion, bell pepper, 1/4 teaspoon salt and 1/4 teaspoon pepper. Cook, stirring occasionally, until the vegetables are soft, about 5 minutes.
Add the spinach, salami, nutmeg, orange zest, the remaining 1/4 teaspoon of salt and pepper. Cook until the spinach is wilted, about 4 minutes. Stir in the bacon and potatoes.
Make 4 indentations in the hash and break an egg into each. Cook until the eggs are cooked through, 5 to 6 minutes.