Bring a large pot of salted water to the boil. Add the pappardelle, return the water to a boil, and cook the pasta until it is almost al dente. Reserve about 1/2 cup of the pasta cooking water; drain.
Meanwhile, in a large sauté pan over medium heat, add the olive oil and sundried-tomato oil. Stir in the radishes and cook, stirring occasionally until very lightly browned, about 5 minutes. Stir in the sundried tomatoes and cook for 2 minutes. Stir in the garlic, oregano, chili flakes, salt and pepper; cook, stirring, for one minute. Add the cream, 1/2-cup of the cheese, the spinach, the drained pasta, and 1/4 cup of the pasta cooking water. Toss well and continue to cook until the pasta is al dente and the spinach is wilted, adding more pasta cooking water as needed if the pasta is too dry. Taste and adjust seasoning, as needed. Transfer the pasta to a serving dish and sprinkle with the remaining cheese.
Makes 4 servings