Bring a large pot of water to a boil over high heat. Salt the water and add the pasta. Cook to al dente and drain.
Heat the extra-virgin olive oil in a large skillet over medium heat. Stir in the anchovy paste and let it melt into the oil. Add the onions and bay leaf and season with salt and pepper, to taste. Cook the onions until very soft and light caramel in color, about 20 minutes. Stir in the cream, and cook until heated through. Remove the bay leaf, then add the pasta and cheese and toss to coat. Transfer to a serving bowl, sprinkle with parsley and serve.