Drain the spinach and squeeze out all the excess water, then chop finely. Place in a bowl and mix in the feta, mascarpone, nutmeg and salt and pepper to taste.
Lay the sheets of filo pastry on top of one another in a pile, brushing each with a little melted butter. Cut out 4 x 15 cm (6 inch) rounds using a saucer as a template.
Divide the spinach mixture between the pastry rounds, spreading the filling out but leaving a 2.5 cm (1 inch) border. Gather the edges up and over the filling to form a rim. Make a shallow well in the spinach mixture.
Transfer the tarts to a baking sheet and bake in a preheated oven, 200°C (400°F), Gas Mark 6, for 8 minutes. Remove from the oven and carefully crack an egg into each hollow. Bake for a further 8–10 minutes until the eggs are set.