In 10-inch omelet pan or skillet over medium heat, heat oil until just hot enough to sizzle a drop of water. Add potatoes. Cook, stirring frequently, until lightly browned. Stir in ham, pepper, onion, and dill weed. Blend thoroughly. With back of spoon, make 4 indentations in mixture. Break and slip an egg into each indentation. Cover and cook over medium heat until whites are completely set and yolks begin to thicken but are not hard, about 5 to 7 minutes. Garnish with cheese, salsa, and dill sprigs, if desired.
(Makes 2 to 4 servings)