Place the livers on pieces of kitchen paper and pat them dry. Trim the livers and cut them into 3 or 4 pieces.
Heat the oil in a large frying pan over a medium–high heat. Add the cayenne pepper, sweet paprika and smoked paprika to the pan and stir for 1 minute. Add the garlic and immediately remove the pan from the heat. Leave the garlic to infuse in the hot oil for about 30 seconds.
Return the pan to the heat and add the liver pieces in a single layer. Cook for around 2 minutes, without moving the pieces, until brown on the underside. Lift the pan from the heat and swirl to mix the juices. Return to the heat, turn the liver pieces over and brown on the other side for about 2 minutes.
Add the tomatoes and tomato purée to the pan and stir. Bring to a simmer then stir in the oil and season with salt and pepper. Reduce the heat and simmer for 10–15 minutes, stirring occasionally until the sauce has thickened and the liver is just cooked through.
Bring a large saucepan of salted water to the boil. Add the pasta and cook for 8–10 minutes, or until cooked but still al dente. Drain the pasta in a colander.
Spoon about a quarter of the liver sauce into a warmed serving bowl. Add the pasta and top with the remaining sauce. Garnish with the parsley and serve immediately.