Remove puff pastry from package and wrapping. Allow to thaw for approximately 40 minutes until it can be opened without cracking.
Place brioche in a bowl, add milk and mix. Set aside.
Begin sweating onions in olive oil. Make a well in the onions, add garlic and saute for a minute. Continue cooking, stirring occasionally, until onions are translucent. Set aside to cool.
Separate two of the eggs. Add the remaining whole egg to the whites.
Add a splash of water to the two yolks and mix together. Set aside.
Place ground pork, soaked brioche, onions (reserve the dirty saute pan), salt, pepper, coriander, nutmeg, whole egg plus two whites, in bowl. Strip leaves from thyme sprigs into bowl. Mix until combined.
Saute a teaspoon or two of the pork mixture in the saute pan. Taste and correct seasoning as necessary.
Roll out first sheet of puff pastry with a dusting of flour and place in a greased 9-inch pie plate. Trim.
Spoon pork filling into crust in pie plate.
Roll out second sheet of puff pastry. Place on top of pie and trim to the edge of the pie plate or a bit wider than that. Tuck the cut end of the crust between the pie plate and the bottom crust. Cut a 1-inch vent in the center of the top crust. Brush the top of the pie with the egg yolk-water mixture. If desired, cut decorative pieces of puff pastry from the trimmings and place on top of the pie. Brush the decorations with the egg yolk-wash.
Bake for 45 minutes at 400°F Use an instant-read thermometer to verify that the filling temperature is 160°F Cook longer if necessary.
Remove from oven and allow to rest for 10 minutes.