Meanwhile, we make the wet rub for the fish. In our mortar and pestle, we put the thyme, cinnamon, allspice, cloves, and brown sugar. We pound carefully, breaking up the whole allspice berries and any sugar clumps. We add the salt and lots of freshly ground black pepper. We pour the mix into a prep bowl.
We rinse and peel our small piece of ginger. Then, using our microplane grater again, we grate the ginger into the rub. We mix with a small spoon to make a wet paste.
We pre-heat our gas grill.
We remove the fish from the fridge, rinse it, and pat dry. We cut it into 3 pieces and place them in the marinade bowl. We turn the steaks over to coat both sides and set it aside for 5 minutes.
When the grill is hot, we remove the swordfish steaks from the marinade, pat dry with paper towels, and place them on a large plate. We rub the oil over the pieces and then coat them with the wet rub on all sides.
We grill for 4 minutes on each side, until just cooked through. We let the fish rest on a clean plate and then serve.