Heat oil in a large frying pan over medium-high heat. Add onions and garlic. Saute, stirring occasionally, for about 2 minutes or until soft and translucent.
Add vegetables and dried oregano. Stir to combine. Season with salt and pepper.
Sprinkle flour over the vegetables. Toss to coat in the flour. Cook, stirring continuously, for about 1-2 minutes or until the raw smell disappears.
Stirring constantly, pour vegetable broth (stock) and milk to make a smooth mixture.
Reduce heat to medium. Simmer for about 5-6 minutes or until slightly thickened. Stir in chopped parsley leaves. Check seasoning. Remove from heat.
Preheat oven to 180C or 350F.
Transfer pie to four 250 ml (1 cup) capacity ramekins. Top with square pastry sheets. Brush the pastry sheets with whisked egg. Bake for 15 minutes or until the pastry puffs and turn golden brown.
Alternatively, you can bake the pie in a large 1 liter baking dish topped with a large sheet of puff pastry. Bake for about 20-25 minutes or until the pastry sheet puffs and turns golden brown.