Heat the olive oil in a medium nonstick skillet over medium heat. Add the leeks, reduce the heat to low, and cook until softened but not brown, about 8 minutes.
Stir the kale into the leeks and cook until just wilted, about 2 minutes. Season the mixture with the nutmeg and some salt and pepper. Stir in the yogurt until combined.
Make four indentations in the kale and carefully crack an egg into each. Sprinkle a little salt and pepper over each egg. Cover the pan and cook the eggs until the whites are completely set and the eggs are cooked desired doneness, 2 to 3 minutes for medium (runny yolk).
Divide the eggs and kale among four serving plates, top each with about 1 1/2 teaspoons Parmesan and serve with the toasted crusty bread on the side.