Preheat the oven to 190°C (Gas Mark 5 / 375°F).
Heat the oil in a large frying pan, and add the sliced mushrooms. Cook over a medium heat for a couple of minutes, until slightly soft.
Add the minced garlic, diced tomatoes, sliced spring onions and as much of the spinach as you can comfortably fit in the pan. Cook for a few more minutes, stirring regularly, until the spinach has mostly wilted. Add the remaining spinach, and again cook until wilted.
Add the cream cheese and crumbled feta, and season with a generous amount of black pepper. Mix well to combine, allowing the cream cheese to melt into the spinach mixture.
Transfer the mixture to a small baking dish. Lay the puff pastry over the top, and press it down securely over the edges of the dish. Trim any extreme excess, leaving about 1cm overhanging the edge of the dish on all sides. Cut a few small slits in the top of the pie, and brush lightly with milk.
Bake the pie for around 25 minutes, or until the pastry top is golden brown and crispy.