Heat the Achiote Oil in a Dutch oven or other heavy 4 to 5-quart pot with a tight fitting lid over medium-high heat. Stir in the Sofrito and alcaparrado and cook until the liquid is evaporated and the Sofrito is sizzling. Season with the salt, pepper, and cumin. Toss in the bay leaves.
Raise the heat to high and add the rice and corn. Cook, stirring, until the rice is coated with the oil and the grains begin to turn "chalky," about 3 minutes. Pour in enough chicken broth to cover the rice by 1-inch. Bring to a boil and cook until the level of the broth meets the level of the rice. Lower the heat to very low, stir the rice thoroughly but only once, and cover. Cook until the rice is tender but with a little bite and all the liquid is absorbed, about 20 minutes. Fluff with a fork before serving.
Heat the oil and achiote seeds over medium heat just until the seeds give off a lively, steady sizzle. Don't overheat the mixture or the seeds will turn black and the oil a nasty green. Once they're sizzling away, pull the pan from the heat and let stand until the sizzling stops. Strain as much of the oil as you are going to use right into the pan; store the remaining oil for up to 2 days at room temperature in a jar with a tight fitting lid.
Place the onion and cubanelle or Italian peppers in the work bowl of a food processor and pulse until coarsely chopped. With the motor running, add the remaining ingredients, 1 at a time, and process until smooth. The sofrito will keep in the refrigerator for up to 3 days. It also freezes beautifully.