For the marinade, mix together all of the marinade ingredients in a large bowl until well combined.
Using a sharp, thin-bladed knife, pierce holes all over the skin of the suckling pig, about 5cm/2in apart.
Place one bin-bag-sized food bag inside another, then place the suckling pig into the bags and pour in the marinade. Shake the bag to cover the pig in the marinade. Squeeze out as much air from the bags as possible, secure tightly, then set aside in the fridge to marinate for 24 hours, turning the suckling pig after 12 hours.
Once the suckling pig has marinated, remove it from the fridge and set aside at room temperature for 6 hours.
When the suckling pig has returned to room temperature, preheat the oven to 190C/170C Fan/Gas 5.
Remove the suckling pig from the bags and transfer it to a large roasting tray. Wrap the head, trotters and tail in aluminium foil, then roast in the oven for 15 minutes, or until the skin is golden-brown.
Reduce the oven temperature to 150C/130C Fan/Gas 2 and continue to roast the suckling pig for 3 hours (for a 5kg/11lb pig) and 4 hours (for an 8kg/15½lb pig). Check the suckling pig every 30 minutes or so to make sure that the skin is not burning, basting it with the roasting juices each time. (If the skin is browning too quickly, reduce the oven temperature by 10 degrees or so.) For the last 30 minutes of cooking time, remove the foil from the pig to brown the head, trotters and tail.
Remove the suckling pig from the oven and pour the roasting juices into a saucepan. Set the pig aside to rest for at least 15 minutes.
Meanwhile, heat the roasting juices over a medium heat. In a small bowl, whisk together 1 tablespoon of cornflour and enough water to form a thick paste with the consistency of double cream. Add the mixture to the roasting juices to thicken them. If they thicken too much, thin with more boiling water if necessary. Stir the ingredients together for 10 minutes, or until the gravy is smooth and has thickened.
To serve, carve the suckling pig at the table, and place the slices onto serving plates. Drizzle over the gravy. Serve with Peruvian-style vegetables and grains, such as quinoa, stir-fried vegetables, fried cassava or roast sweet potato.