In a small saucepan, melt the butter over medium heat. Add the garlic and sauté for 1 minute until it just turns golden. Whisk in the cream and bring to a simmer. Season with salt (go lightly because of the salty tapenade) and pepper, then simmer for about 8 minutes until it its reduced and thickened. Whisk in ½ cup of the grated Parmesan.
Meanwhile, bring a large pot of salted water to a boil. Cook the fettucine according to package directions, adding the cut green beans during the last two minutes of cooking. Drain the pasta and green beans.
Return the cooked pasta and the beans to the same pot, and pour in the hot alfredo sauce. Toss to coat the pasta and beans well.
Immediately turn the pasta and beans into a shallow serving dish or plate it up in individual bowls. Give a final grind of black pepper, dollop over the tapenade, sprinkle over the remaining Parmesan and either toss yourself, or let each diner toss their serving. Sprinkle with parsley as desired and serve hot.