Using a large chef’s knife, remove the snapper head and tail and set aside. Cut the rest of the fish crosswise through the spine into 2-inch-wide pieces. Place the fish head, tail, and pieces in a large bowl and refrigerate.

Make the broth: In a large pot, heat the oil over high heat until it just begins to shimmer. Add the onion and cook, stirring frequently, until translucent, about 4 minutes. Add the garlic and cook until fragrant, about 1 minute more. Stir in the plum tomato and continue cooking until most of the liquid has evaporated, 3–4 minutes. Add the stock, tamarind, fish sauce, chiles, sugar, and sinigang seasoning, bring to a boil, then turn the heat to low to maintain a strong simmer. Cook until the broth has reduced slightly, the onions are very soft, and the flavors have melded, about 30 minutes. Adjust the seasoning to your taste with more tamarind extract or fish sauce if desired, then set a fine mesh strainer in a large bowl or heatproof container and strain the broth, discarding any solids. (The broth can be used immediately, or may now be cooled to room temperature and stored, tightly covered, in the fridge for up to 3 days or the freezer for up to 1 month.)

When you’re ready to finish the singigang, pour the broth into a large, wide pot and bring to a boil over high heat. Turn the heat down to low to maintain a gentle simmer, then add the fish pieces (including the head and tail) and cook without stirring, until the fish flesh begins to feel firm, 3–4 minutes. Add the cherry tomatoes, shallots, long beans, okra, eggplant, and daikon and continue cooking until the fish is just cooked through and the vegetables are tender but still crisp and vibrant, about 3 minutes more. Remove from the heat, stir in the yam leaves, and set aside until the greens have wilted.

To serve: Divide the fish pieces and vegetables among 6 wide soup bowls. Top each with some of the broth and serve with steamed jasmine rice on the side.