Rub the steak with the olive oil and season. Heat a large frying pan over high heat until searing hot. Cook the steak on each side for 1 minute, then set aside on a plate to rest and cool.
Place the spinach in a large pan with 3 tbsp of water. Cover the pan and place over a medium-low heat, stirring occasionally for 2-3 minutes, until the spinach has wilted. Squeeze out any extra moisture, then tip into a small bowl, add a pinch of freshly grated nutmeg and some seasoning. Leave to cool.
Preheat the oven to 200°C, 180°C fan, gas 6. Roll out the puff pastry on its paper and then roll it slightly thinner with a rolling pin. Cut in half vertically.
Divide the mushroom pate in half, and spread down one half of each piece of pastry. Place the spinach on top of the mushroom pâté.
Cut the steak into long strips, about 1cm wide, then lay on top of the spinach.
Carefully fold the empty half of the pastry over the filling, and press down gently, using a little of the beaten egg to seal, making sure it’s quite tight around the filling. Transfer to a lined baking tray, and repeat with the other one.
Brush the pastry with the beaten egg and cook in the oven for 20 minutes, until the pastry is puffed and golden.