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1
Place the oxtail sections in a large pot of cold water, starting cold rather than dropping them into boiling water so the impurities are drawn out gradually into the water rather than seized on the surface of the meat. Bring to a boil and blanch for 15 minutes. Drain and rinse each piece thoroughly under cold running water, removing all grey scum and residue — the rinsed oxtail should show clean, pale-pink flesh at the cut surfaces, which is the condition for a clear broth.
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2
Dry the blanched oxtail sections with a cloth, since any surface moisture will steam the meat in the pan and prevent a proper crust from forming. Heat the lard in a heavy braising pot over medium-high heat and brown the oxtail in batches, without crowding, turning to caramelise all surfaces deeply — each side requires several minutes of undisturbed contact, and the sections are ready to turn when they release cleanly from the pot. The finished crust should be a dark mahogany on every surface; this Maillard crust is the structural depth of the finished broth.
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3
Reduce the heat to medium and, in the fat remaining in the pot, fry the sliced shallots and garlic until softened and lightly coloured, stirring frequently so they sweeten evenly without scorching. Add the tomatoes and cook until they collapse completely and the oil begins to separate from the solids at the pan edge, which tells you the water in the tomatoes has cooked off and their sugars and acids have concentrated. The mixture should smell sweet and rounded at this point, with no raw sharpness remaining.
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4
Return the browned oxtail to the pot and add the stock or water, bruised lemongrass stalks, sliced galangal, fresh red chili, cracked black pepper, soy sauce, star anise, and cinnamon — bruising the lemongrass first opens the fibres so its fragrance passes into the broth rather than staying locked in the stalk. Bring to a gentle simmer, then skim the fat and foam that rises to the surface. Reduce the heat to the lowest setting that maintains a bare simmer, small bubbles breaking at the surface and never a rolling boil, so the broth stays clear and the meat is coaxed apart slowly rather than hammered tough.
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5
Braise uncovered or partially covered for a minimum of 3 to 4 hours, skimming fat at each 45-minute interval so the broth does not turn greasy and opaque. This is where the dish lives or dies: after 3 hours, lift a spoonful of broth and allow it to cool on the spoon for 30 seconds — the broth must feel slightly sticky and viscous against the lip, and if it remains thin and watery the braising must continue. The oxtail sections should yield to gentle pressure at the thickest point, the meat beginning to part from the bone without force.
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6
Remove the lemongrass stalks, cinnamon stick, and star anise, then taste and adjust seasoning. Cool the braise to room temperature and refrigerate overnight so the fat rises and solidifies into a single layer that can be lifted away cleanly the next day, a task that is almost impossible to do as thoroughly with warm liquid fat. The broth beneath should have set to a firm, amber jelly, confirming that the long braise has drawn everything it can from the bones.
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7
Reheat gently until the broth is fully liquid and the oxtail is heated through. Ladle into deep bowls, placing two or three oxtail sections in each, and spoon the broth over generously. Garnish with fried shallots and sliced green onion, and serve with calamansi halves and freshly cut bird's eye chili on the side — the broth should appear deep amber-brown, glossy, and clear, never murky.