Season the fish: Massage the tambakol pieces with salt and pepper and let them marinate for at least 15 minutes to enhance flavor and reduce splattering when frying.
Fry the fish: Heat oil in a pan over medium heat and fry the tambakol pieces until half-cooked, about 2-3 minutes per side. Remove the fish from the pan and set aside.
Create the flavor base: In the same pan with the remaining oil, sauté the onions, garlic, and ginger until fragrant and soft, about 2 minutes. Add the diced tomatoes and gently crush them with your spoon to release their juices and flavor.
Prepare the coconut sauce: Pour in the coconut milk and add the whole green chilies. Bring to a gentle boil over low heat. Season with pepper and fish sauce to taste. Simmer for 5-7 minutes until the sauce begins to thicken.
Combine with fish: Return the fried fish to the pan and simmer for 5-7 minutes until the sauce is reduced and the fish is fully cooked.
Add greens: Stir in the chopped pechay or mustard leaves and cook just until slightly wilted, about 1-2 minutes.
Serve: Transfer the ginataang tambakol to a serving plate and enjoy with steaming hot rice.