Remove the stems from the portobello mushrooms (set them aside for later), and place the mushrooms face down on a baking tray. Drizzle lightly with oil, and roast at 190°C (Gas Mark 5 / 375°F) for around 25 minutes, until they are soft and have released all of their liquid.
Finely chop the mushroom stems, and add them to a large frying pan along with the crumbled haggis, the thyme leaves and the finely chopped kale. Cook over a medium heat for 5-10 minutes, stirring regularly, until the mushroom stems and kale have cooked right down and the mixture is well combined.
When the haggis mixture and the portobello mushrooms are cooked, set both aside to cool - you can put them in the fridge for a while if you like. Ideally you want them to be completely cool before you add them to the pastry, but a little bit of remaining heat is okay.
If needed, roll the pastry out to form a rectangle measuring approximately 16 x 11 inches - it'll be easier later if you do this on a sheet of baking paper. Add about two thirds of the cooled haggis mixture along the centre of the pastry, and form into a log shape (see photos if needed). Lay the roasted portobellos on top, and finish with the remaining haggis mixture. Press it down firmly to give a solid log shape.
Fold the short ends of the pastry over the filling (you can cut away any excess pastry from the corners if you like), then the long edges. Seal by pressing the pastry together.
Carefully turn the wellington over onto a lined, greased baking tray, so that the join in the pastry is underneath (I found it easiest to do this by laying the lined baking tray on top of the wellington, lifting the sheet of baking paper that the wellington was sitting on, and then quickly flipping it over.
Cut several slits in the top of the wellington, and brush with milk.
Bake at 190°C (Gas Mark 5 / 375°F) for around 35-40 minutes, or until the pastry is golden brown and crispy all over. Cut into slices to serve.