Whisk together the egg, heavy cream, parmesan, dried minced onion, salt, and pepper until smooth.
Stir in the chopped ham and shredded cheddar.
Press two brioche slices into a square dish, forming a deep well in the center of each.
Spread a thin layer of butter over each well.
Spoon the filling into the wells and top with parsley, if using.
Air fry at 335-340°F (170°C) for 8-9 minutes, until the edges are golden and the filling is just set. Let rest 1-2 minutes before serving.