Melt butter in a large skillet over medium heat until foaming. Add ham slices and cook, turning occasionally, until heated through, golden brown, and crisp on both sides. Transfer to a paper towel-lined plate to drain.
Divide English muffin halves between 4 plates. Place 1 ham slice on each English muffin half and top with one drained egg. Season eggs with salt and pepper.
Spoon warm hollandaise over each egg. Sprinkle with parsley or chives (if using) and serve immediately.
