Pre-heat oven to 200 degrees C (400 degrees F). Peel and parboil the potatoes whole. Allow to cool slightly and slice thinly. Break the broccoli in to florets and also slice so they are reasonably thin to allow you to layer the potato and broccoli.
Combine the potato, broccoli and sage in a large bowl or on a board, being careful not to break up the potato, and add a good few glugs of olive oil so everything is well coated. Season well with salt and pepper.
Place the filling in the centre of the pastry, layering the potato and broccoli, leaving a boarder to fold over the filling. Fold over the edges and secure with a little water if it isn't sticking. Brush with the egg and milk mixture and bake for 50 minutes or until lovely and golden. Serve