Increase your oven temperature to 220°C/200°C fan/gas 7. Once the pumpkin is cool, push it through a sieve into a large bowl to create a smooth purée. In a separate bowl, whisk together the caster sugar, salt, nutmeg, and half of the cinnamon.
Stir the beaten eggs, melted butter, and milk into the spice mixture, then add this to the pumpkin purée and stir until everything is well combined. Pour the filling into the cooled tart shell and bake for 10 minutes. After this initial bake, reduce the oven temperature to 180°C/160°C fan/gas 4 and continue baking for another 35–40 minutes, until the filling is just set; it should still have a slight wobble in the center.