Place potatoes in a large glass bowl; cover and microwave on HIGH for 4 minutes.
Meanwhile, cook bacon in a large deep skillet over medium heat until crisp. Remove bacon to drain on paper toweling; drain all but 3 tablespoons fat from the skillet.
Add bell pepper, onion, and garlic to skillet. Cook and stir over medium-high heat until tender. Stir in par-cooked potatoes, ham, and cooked bacon. Season with salt and pepper; cook and stir 4 minutes longer.
Add spinach to skillet; cover and cook until wilted. Continue cooking until hash is browned on bottom.
Make 4 wells in center of the hash; crack an egg into each well. Reduce heat to medium and cook about 5 minutes or until eggs are set. Sprinkle with dill and more freshly ground pepper, if desired.