Bring a large pan of salted water to the boil and add the pasta. Cook according to packet instructions until al dente. Add the peas for the last minute. Drain and reserve one cup of the cooking water.
Start by removing the skin from the chorizo ring and discarding it. Cut the chorizo into small 1-2cm size chunks. Cut the halloumi into pieces a similar size.
Put the chorizo into a large frying pan over a medium heat. Cook for 2 minutes, stirring often, until it starts to release the oil.
Add the halloumi to the frying pan and cook for 10 minutes, stirring often (but gently, so that you don’t break up the halloumi too much) until it is golden brown.
Add the tomato puree, reduce the heat to low and stir. Add 100ml water, stir to mix and let it reduce a little, then add the double cream. Stir gently. Taste the sauce and season - you probably won’t need any salt, but you may want to add pepper.
Combine the pasta, peas, pasta water and sauce. Mix well, then let it sit for 2 minutes before serving.