Combine the split peas, garlic, bay leaf and potato in a saucepan and cover with water. Bring to the boil over medium heat and cook for 25–35 minutes or until the peas are tender. Drain, reserving some of the cooking liquid.
Place the peas and 100 ml of the olive oil in a food processor. Season to taste and process until smooth, adding a little cooking liquid if necessary to make a semi-smooth paste.
Preheat the oven to 220°C.
Carefully loosen the skin of the spatchcocks to make pockets and insert four to six slices of chorizo and a sprig of oregano in each. Season with salt and pepper.
Heat the remaining olive oil in a large ovenproof frying pan or flameproof baking dish over high heat. Add the spatchcocks and brown on both sides. Add a knob of butter, the shallots, garlic cloves and chilli and cook for 3 minutes. Stir in the vinegar, bring to the boil and simmer for 10 seconds.
Pour in the chicken stock and boil for 2 minutes, then transfer the pan or dish to the oven and roast the spatchcocks for 8–10 minutes or until cooked and golden.
To serve, spoon the split pea paste onto plates and top with the spatchcocks.
Bring the pan juices to the boil over medium heat. Cook, stirring, until the mixture has reduced to a sauce consistency, then pour over the spatchcocks. Garnish with the parsley sprigs, if using.