For the pastry: Combine the flour, butter, and salt in a food processor; pulse several times until the mixture resembles rough breadcrumbs.
Add the egg and pulse until a rough dough forms around the blades; if the dough is too dry, add iced water by the tablespoon, pulsing between additions until the dough comes together.
Turn out the dough onto a work surface and shape into a disc with floured hands. Wrap in clingfilm and chill for 1 hour.
After chilling, preheat the oven to 180°C (160° fan) | 350F | gas 4. Set the pastry on the work surface to soften slightly.
For the filling: Blanch the asparagus in a saucepan of salted boiling water for 1 minute. Drain and rinse under cold water for 1 minute.
Spread out on sheets of kitchen paper to absorb any excess water; cut crosswise into bite-sized pieces.
Crack the eggs into a large mixing bowl. Add the milk, crème fraîche, 1/2 tsp salt, some freshly grated nutmeg, and freshly ground black pepper; thoroughly whisk to combine the filling.
Dust a work surface and a rolling pin with some flour. Divide the dough into four and shape into balls; roll out each ball into a 1/4-cm | 1/8-inch thick round.
Drape the pastry into four individual fluted tartlet tins, pressing the pastry into the base and up the sides; trim any excess overhanging pastry. Transfer the tins to a large baking tray and prick the bases all over with a fork.
Divide the asparagus and watercress between the lined pastries. Use a ladle to carefully fill each pastry with the egg filling.
Bake until the pastry is cooked through and the filling is golden and puffed, 30-40 minutes.
Remove from the oven and let the quiches cool in their tins. Turn out and serve warm or at room temperature with a garnish of watercress.