Heat a dash of oil in a large pan, and add the diced onion and carrots. Cook over a medium heat for a few minutes, then add the mushrooms, asparagus, pepper, peas and sweetcorn. Cook for another 10 minutes, stirring regularly, until the vegetables are fairly soft.
Meanwhile, add the diced halloumi to a separate frying pan (you don't need any oil), and spread it out into a single layer if possible. Let it cook for a few minutes, stirring occasionally, until it has released its liquid, and the liquid has been cooked off. Allow the halloumi to turn golden brown all over, and add to the cooked vegetables.
In the same pan as you cooked the halloumi (or a new pan if you prefer), melt the butter over a low heat, and add the flour. Mix well to form a roux, and cook for 1 minute. Add the milk a little at the time, stirring constantly, and allowing the mixture to come together into a smooth paste each time before adding more milk. When you've added all of the milk and your sauce is smooth and creamy, add the oregano and plenty of black pepper (you probably won't need any salt, as the halloumi cheese is salty). Mix the white sauce in with the vegetables and halloumi, and set aside to cool.
Lightly spray an 8-inch springform cake tin with oil (or grease with butter).
Roll out the pastry with a little flour (even if you buy ready-rolled, it's nicer if you roll it just a little thinner). Lay one of the sheets loosely over the cake tin, and slowly ease it into the tin, pressing gently into the corners. Prick the bottom of the pastry several times, and blind bake for around 15 minutes at 190°C (Gas Mark 5 / 375°F), until slightly golden. Leave to cool.
When the pastry case and the creamy filling are both mostly cool (a small amount of residual heat is okay), add the filling to the case. Lay the other sheet of pastry over the top, and crimp around the edges. Trim any excess pastry, and use the trimmings to create a pattern on top of the pie if desired. Make a small hole in the top of the pie so the steam can escape.
Brush the top of the pie lightly with milk, and bake at 190°C (Gas Mark 5 / 375°F) for around 45 minutes, or until the pie is golden brown and crispy all over.
Carefully remove the pie from the cake tin, and serve. For neater slices, allow the pie to cool for at least 10 minutes before slicing.