Preheat a grill to medium-high and lightly oil the grates or preheat the oven to 400 degrees F.
Grill or roast the yams for 40 to 60 minutes, or until tender.
For the mullet:
Meanwhile, heat the oil, covered, in a large heavy-bottomed saute pan over medium-high heat. Season the fish with the all-purpose seasoning blend, add the fish in the pan, and sear to brown for around 2 minutes per side. After this, reduce the heat down to medium-low. Drop in the green onion, onion, tomato, okra, chile, vinegar, soy sauce, thyme, and butter, using more or less of the fat depending on how rich you want the dish to be. Cover the pan with a lid, and simmer over moderate heat for 30 minutes.
Once the yams are fully cooked, peel and discard the skins or scoop out the flesh. In a small bowl, combine the yams with the mayonnaise. Season the yams with salt, and pepper, if desired, and serve alongside the fish and sauce.
*Homemade all-purpose seasoning is made up of equal parts ground allspice, ground ginger powder, and grated nutmeg.