Bring 3cm water to a simmer in a small pot. Set a heatproof bowl over it without touching the water.
Whisk yolks and lemon juice in the bowl for 2 minutes until pale and thick.
Slowly pour the warm melted butter in a thin stream, whisking constantly. The sauce should emulsify and thicken. Add hot water to loosen if needed.
Season with cayenne and salt. Keep over warm water off the heat until ready.
Assemble
Toast muffins, butter them. Warm the ham in a dry pan for 30 seconds per side.
Bring a deep pan of water with vinegar to a gentle simmer. Crack an egg into a small cup. Swirl the water and slide the egg in. Cook 3 minutes for a runny yolk. Scoop out with a slotted spoon onto paper towel. Repeat.
Place 2 muffin halves on each plate. Top with ham, a poached egg, and generous hollandaise. Scatter chives. Serve immediately.