Preheat oven to 180C/160C fan forced. Line a large baking tray with baking paper. Use a small serrated knife to cut each bread roll into 8 wedges, without cutting all the way through (leave the base intact).
Use electric beaters to beat the cream cheese and sugar in a bowl until smooth. Add the cream and beat until combined. Transfer mixture to a piping bag fitted with a 1cm plain nozzle. Pipe cream cheese mixture in the cuts of 1 bread roll, starting from the centre and piping to the outer edge. Repeat with remaining cream cheese mixture and rolls.
Whisk together the butter, garlic, egg and milk in a bowl until combined. Line an air fryer basket with baking paper. Place 2 filled breads in the air fryer. Drizzle over one-third of the butter mixture and sprinkle with one-third of the parmesan. Cook at 180C for 8 minutes or until golden and filling is set. Repeat with the remaining breads, butter mixture and parmesan.
Sprinkle with parsley. Serve warm.
