Remove any membrane from the liver (as explained in the video), cut into 1 to 2 inch pieces, rinse, then soak in the milk for at least 2 hours. While we would normally wash the liver with lime or lemon juice following Caribbean traditions, this milk method works better in my opinion. It helps to eliminate that sort of chemical or metallic taste liver is known for, removes any unpleasant odor, and helps maintain a lovely moist texture when cooked.
Rinse the soaked liver, drain well, and season with salt, black pepper, green seasoning, and Caribbean browning.
Heat the olive oil in a wide pan over medium heat and add the seasoned liver pieces. Sear on all sides for 3–5 minutes uncovered to burn off excess liquid.
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Rinse the bowl used to marinate the liver with 1 cup of water and set aside.
Add the onion, scallions, garlic, ketchup, additional green seasoning, tomato, and oyster sauce. Stir well to combine and add the optional thyme and ginger if using.
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Pour in the reserved water, bring to a boil, then reduce to a rolling simmer with the lid on for 15 minutes.
Taste and adjust salt as needed. Remove the lid and continue cooking to reduce and thicken the sauce to your liking. Under 5 minutes in most cases.
Finish with chopped parsley and serve.