Shuck the oysters, reserving the liquid. Place the oysters and liquid in a saucepan. Reserve the deeper half of each oyster shell. Cook the oysters over medium heat for about 30 seconds, just to give them some firmness. With a slotted spoon, remove the oysters to a bowl and set aside. Add the cream to the oyster liquid in the pan and cook for 10 minutes to reduce. Add the mustard and half the cheese. Set aside.
In another saucepan over low heat, cook the spinach with 1 tablespoon (15 ml) water until wilted. Strain the excess spinach water into the cream mixture and set the spinach aside. Mix the remaining 1/2 cup cheese and the breadcrumbs in a bowl and season with salt and pepper.
Heat the broiler. Arrange the oyster half-shells in a flameproof casserole dish filled with seaweed or large rock salt. Place each oyster in a shell and add a bit of the cream mixture and some spinach. Top with the breadcrumb mixture. Broil until the cheese melts and the tops are lightly browned, about 1 minute.