Roll out the dough and line a tart ring or pie pan with the dough. Chill for 30 minutes.
Blind bake the tart shell by laying parchment paper or foil (sized slightly larger than the pie pan) over the dough and placing pie weights or dry beans on top of the paper. Bake until the crust is light brown. Remove the parchment paper and weights. If any part of the dough looks raw, return it to the oven for a few minutes without the weights and parchment and cook until lightly browned. Let the pie shell cool. Lower the oven temperature to 250°F.
Trim the asparagus tips and set aside. Thinly slice the rest of the asparagus.
Thinly slice the pale part of the leek.
Heat the oil in a large skillet over medium high heat. Add the leeks and cook until soft. Add the asparagus slices and tips and cook for another minute until tender. Add the peas and remove from the heat.
In a medium bowl, whisk together the milk, cream, and eggs. Strain the mixture through a sieve. Add the nutmeg and then salt and pepper to taste.
Cover the bottom of the pie shell with the vegetable mixture and the cheese in an even distribution.
Pour the egg mixture over the vegetables and cheese. Bake for 20-30 minutes or until the filling is set.
This is enough filling if you are using an 8 or 9-inch tart ring. If you are using a pie pan, you may want to add an extra egg + 1/4 cup milk since the pan is deeper.