Take the frozen filo out of the freezer at least an hour before beginning.
Start by making the filling. Cook the broccoli, carrots, leeks and mushrooms in a large skillet with a lug of olive oil and salt, over medium-high heat until softened.
Make the béchamel (directly over the veggies).
Add 3 slightly overlapping filo sheets for the base making a big rectangle. Keep going until you have used all the filo.
Add the filo in the center of a baking dish of your choice. Add the filling. Cover it with the sides of the filo until the filling is well covered.
Bake in the oven on the lower level until the filo is lightly golden. Let cool down.