To make the filling, sauté diced onion, garlic, and carrot in vegetable oil at medium heat until slightly softened.
Add vegan mince, roughly chopped mushrooms, along with tomato paste, curry powder, mustard powder, thyme, nutmeg, and black pepper. Stir together and cook for a few minutes until mince is browned and mushrooms have softened.
Add lentils and vegetable broth and let simmer for 5-7 minutes until lentils have softened.
Mix corn flour and water together and add to filling, stir well, and once any remaining liquid has thickened into a gravy-like consistency, remove from heat and allow to cool slightly while preparing pastry. If filling is too dry add a little extra broth or water.
Preheat oven to 200 fan/220 C/425 F.
Transfer filling into one family size pie dish or two smaller dishes.
Roll out enough puff pastry to cover pie dish, to about 1/4-1/2 cm thickness.
Brush the edges of the pie dish with water and lay puff pastry on top of the dish. cut around the edge with a sharp knife to remove excess dough and firmly press pastry down around the edge of the dish to seal.
Generously brush the top with plant milk and cut several small slits in the middle to allow the air to escape.
Bake pie for 40 minutes until pastry top is golden and flaky. Remove from oven and let stand for a few minutes before serving with your choice of vegetable side dishes and gravy.