In a small bowl, use the fork to mash together the butter, herbs, shallot, lemon juice, salt and several grinds of black pepper, and the nutmeg until the butter has absorbed the lemon juice.
Season the fish with salt and pepper. Cut four large sheets of parchment paper, each about 12 x 15 inches. Place each fillet on a parchment sheet. Top each fillet with a quarter of the butter mixture and a quarter of the spinach leaves. Season the spinach lightly with salt and pepper.
Fold the parchment over the fish and spinach. Crimp and tightly fold the edges of the parchment to create a sealed packet. (It doesn’t matter exactly how you crimp or fold the parchment - the aim is just to seal the packet. Sometimes I staple the packets closed instead of folding them, which is easier if not quite as elegant.)
Arrange the packets on two large rimmed baking sheets and bake for 8 to 12 minutes, depending on the thickness of the fish. You can check one for doneness by opening the corner of the packet and poking the fish with a fork (it should slide easily) – then make sure to serve that opened packet to yourself. Transfer the packets to serving plates. Allow your guests to tear or cut open the parchment themselves (watching out for a sudden waft of steam), and serve the lemon wedges and flaky sea salt on the side.