Preheat the oven to 200°C/gas mark 6. Heat the oil in a large pan, add the mushrooms and cook for 5-8 minutes. Stir in the garlic and spinach, and cook for a further 2 minutes. Drain off any excess liquid.
Meanwhile, bring a pan of water to the boil and add the 4 whole eggs. Boil for 7 minutes, then drain and cool under running water. Peel the eggs.
Put the rice in a bowl. Season with freshly ground black pepper, then stir in the dill.
Dust your work surface with the flour and roll out the pastry to a square. Spoon the mushroom mixture down the middle, put the boiled eggs on top and spoon over the rice. Brush the pastry around the filling with the beaten egg, then fold the long sides up and over the filling. Flip the roll over, trim the edges and crimp together with the back of a fork. Use any trimmings to decorate the roll. Put on a baking tray, brush with the remaining egg and bake for 30 minutes until golden.
Slice the roll and serve warm with the Italian salad.