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1
Combine the fish heads, carcasses, and shellfish with cold water in a pot. Bring to a simmer and cook until a concentrated, deeply flavoured fumet is achieved. Season the stock boldly — bomba rice absorbs a large volume of liquid and will carry the seasoning. Strain. Reserve the cooked fish aside. The stock is ready when it is rich, clear, and carries full flavour of the sea.
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2
Steep the saffron in a ladleful of the hot fumet. Keep the remaining fumet at a gentle simmer throughout cooking.
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3
Warm the olive oil in a wide, flat pan over medium heat. Cook the sofrito — tomato and onion — until it is completely soft, reduced, and beginning to darken at the edges. The sofrito is done when almost all moisture has left and the mass is deep in colour.
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4
Add the bomba rice to the sofrito and stir to coat every grain in the oil and tomato base. Add the saffron and its steeping liquid. This is where the dish lives or dies: add the hot fumet in one confident measure — bomba rice demands a generous, well-seasoned stock — then do not stir again. From this point, the rice must be left entirely undisturbed.
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5
Cook over steady heat, without stirring, until the liquid is absorbed and the rice is cooked through. In the final minutes, raise the heat briefly to form the socarrat — the toasted crust on the base of the pan. The socarrat is ready when a faint crackling is heard from the base of the pan and a faintly nutty, toasted smell rises.
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6
Remove from heat and rest the pan briefly. The rice is done when the grains are swollen and separate, holding their structure, with no raw starch at the centre. Serve the rice directly from the pan. Serve the reserved fish a banda — on the side — with alioli alongside. The dish is incomplete without it.