Place the salted cod in a bowl, cover it with cold water, and refrigerate for 8 to 12 hours. Change the water at least twice during soaking. Drain and rinse the fish well. This soaking time is not included in the total time.
Put the soaked cod in a small saucepan and cover with fresh water. Bring to a gentle boil, simmer for 8 to 10 minutes, then drain. When cool enough to handle, remove any bones or skin and flake the fish into bite-size pieces. Taste a small piece; if it is still too salty, repeat the simmering step in fresh water.
Heat the oil in a large skillet over medium heat. Add the onion and bell pepper and cook, stirring occasionally, until softened.
Add the scallions, garlic, tomato, thyme, optional Scotch bonnet, and black pepper. Stir for about 1 minute, until fragrant.
Add the chopped callaloo or spinach in batches, stirring as it wilts. Cook until the greens are tender and most excess moisture has cooked away.
Fold in the flaked salt cod and cook just until heated through. Taste before adding anything salty; salt is usually unnecessary. Remove the thyme stem, if using, and serve with lime wedges if desired.