Step 1Spread the livers on paper towels and pat them dry. Trim the livers and cut them into 3 or 4 pieces.
Step 2In a large skillet, heat the canola oil over medium-high heat. Add the cayenne pepper and sweet and smoked paprika to the oil and stir, then add the garlic. Immediately remove the pan from heat and leave the garlic to warm in the hot oil until fragrant, about 30 seconds.
Step 3Return the pan to heat. Add the livers in a single layer and cook them, without moving, until they are browned on the bottom, around 2 minutes. Remove the pan from heat and swirl it to mix the juices. Return to heat, turn the livers and brown on the second side for about 2 minutes more.
Step 4Add the tomatoes with their juices and the tomato paste to the skillet and stir with a wooden spoon to loosen any browned bits in the bottom of the pan, and to break up the tomatoes. Bring to a simmer, then stir in the olive oil and season with a heaping ½ teaspoon salt and several grinds of pepper, or to taste. Reduce the heat to medium-low and simmer, stirring every few minutes, until the sauce has thickened slightly and the livers are just cooked through, 10 to 15 minutes.
Step 5Bring a large pot of water to a boil over high heat. Add a tablespoon or so of coarse salt. Stir in the pasta and cook, stirring every 2 minutes, according to the package directions until the pasta is al dente, about 8 minutes depending on the brand.
Step 6Place the pasta serving bowl in the sink and set a colander inside. Drain the pasta into the colander, then return it to the cooking pot. Leave the hot pasta water in the serving bowl long enough to warm it, about 30 seconds. Empty and dry the serving bowl.
Step 7Spoon about ¼ of the sauce into the serving bowl. Add the pasta and top with the remaining sauce. Coarsely chop the parsley and sprinkle it over the pasta. Mix at the table and serve immediately.