Boil the salted cod in a pot of water for about 20 minutes to remove the salt. Drain and rinse the fish, then shred it into small pieces.
Peel, core, and cube the honey nut squash, then place in a bowl with cool water to prevent discoloration.
Heat olive oil in a heavy pot over medium heat. Reduce to low, then add onion, garlic, and a pinch of black pepper. Sauté for 2–3 minutes.
Add the prepared salted cod and stir well. Mix in the Caribbean green seasoning and continue stirring.
Increase the heat to medium-high. Add the drained squash cubes and stir thoroughly to combine.
Sprinkle in the brown sugar, cover the pot, and cook for 3–5 minutes. The squash will begin to release its natural juices.
Add salt, reduce the heat to low, and cover. Simmer for 20–24 minutes, stirring occasionally, until squash is soft and beginning to break apart.
Taste and adjust salt if needed. Raise the heat to medium-high to evaporate excess liquid, using the back of a spoon to mash any remaining solid pieces. Cook an additional 5–7 minutes until desired texture is reached.
Serve hot, either as a side dish or with roti.