Using your fingertips, press a bread slice down in the centre to make a shallow well, leaving a ½-inch edge along crust. Repeat with remaining bread slices.
Spread butter and Dijon evenly over wells and top edges of bread slices.
Fill slices evenly with prosciutto, Gruyère, tomato and parsley. Place bread slices into basket of an air fryer. Pour egg into each well until just filled.
Air fry at 350°F (180°C) for 8 to 10 minutes or until egg is set. (Alternatively, place on a parchment paper-lined baking sheet and bake in an oven at 375°F (190°C) for 5 minutes or until egg is set).
Garnish with pepper to taste and parsley.
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