First, bring a large pot of salted water to a boil. Add the penne and cook until al dente, then drain and set aside. Return the pot to the stove.
Add olive oil, garlic, and artichokes to the pot over medium heat. Season with salt and pepper, and cook until artichokes are slightly softened, about 3 to 5 minutes.
Next, add the spinach, heavy cream, cream cheese, shredded mozzarella, and grated parmesan to the pot. Lower heat to medium-low and cook, stirring constantly and gently, until the spinach is wilted and the cheese is melted, about 3 to 5 minutes.
Finally, stir the pasta back into the pot to coat evenly in the spinach and artichoke cheese sauce. Serve immediately.