Preheat oven to 180°C/160°C fan forced. Lightly grease a 1.25L (5 cup) pie dish.
Whisk together butter, egg yolks and sugar for 1 minute or until well combined and slightly paler. Add the flour and gently whisk until combined. Gradually add the milk, whisking constantly, until combined. Stir in the Baileys.
Use electric beaters to whisk the egg whites in a clean, dry bowl until soft peaks form. Add to butter mixture. Use whisk to fold egg whites and butter mixture together until just combined. Carefully pour into prepared dish. Place dish on a baking tray.
Bake for 55 minutes or until pie is golden brown and still has a slight wobble in the centre. Remove from baking tray and set aside in dish to cool (see notes). Drizzle over extra Baileys to serve.
