Preheat the oven and prepare a baking dish. Preheat the oven to 200°C/180°C Fan/Gas 6. Prepare a fairly deep 28cm (11in) diameter dish or a 3-pint dish.
Cook the green veggies. Break the cauliflower into small, even-sized florets, including chopping some of the smaller leaves. Bring a large pan of salted water to a boil. Boil leeks for 4 minutes, then add cauliflower florets and leaves, boiling for an additional 3 minutes until just tender. Drain, run under cold water to stop cooking, and set aside.
For the cheese sauce. Melt butter in a large saucepan over medium heat. Add flour, stirring for 1 minute. Gradually whisk in hot milk until thickened. Stir in mustard, Cheddar, Parmesan, salt, and freshly ground black pepper. Let it cool for 5 minutes.
Pan-fry the mushrooms. Heat butter over high heat, pan fry mushrooms for 3 minutes until golden, season with salt and pepper, and set aside to cool.
Mix all the veggies and put them in the baking dish. Add all cold vegetables and frozen peas to the cheese sauce, stir, and check seasoning. Spoon into the pie dish.
Cover the baking dish with pie crust. Unroll the pastry and set aside a 7cm (2¾in) strip from the short side, chilling it in the fridge. Roll out the remaining pastry slightly larger than the pie dish. Brush the beaten egg around the dish's edge, place the pastry on top, and press down on the edges to seal. Trim any excess pastry with a sharp knife, make a small slit in the centre for steam to escape, and brush the top with a beaten egg.
Decorate the pastry and bake. Roll out the reserved pastry strip a bit thinner, then roll it up tightly. Using a sharp knife, slice it into long, thin strips. Unravel and dip them into the egg wash, then arrange on top of the pie in a random pattern. Bake in the preheated oven for about 40–45 minutes, until the pastry is golden, and the sauce is bubbling around the edges.