Cut a large circle (approx. 9 cm Ø) from each toast slice. Roll circles flat with a cake roll. Grease the hollows of a muffin tray and line them with the toast slices.
Peel and finely chop the onion. Heat the oil in a pan. Sauté onion for 2-3 minutes, add diced ham and continue to fry for about 2 minutes. Spread the ham mix into the toast hollows.
Grate cheese. Whisk eggs and milk and season with salt and pepper. Fill egg milk into the wells and sprinkle with cheese. Bake in a preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: see manufacturer) for approx. 20 minutes until golden brown.
Take the muffins out of the oven and remove them from the troughs. Sprinkle with parsley before serving. Serve lukewarm or cold.