Heat the olive oil and butter in a large pot or Dutch oven over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant (don't let it burn!).
Add the uncooked pasta, chicken broth, salt, and pepper to the pot. Stir everything together and bring to a boil.
Reduce heat to medium-low and simmer for 12-15 minutes, stirring frequently to prevent sticking, until the pasta is al dente and most of the liquid has been absorbed.
Stir in the heavy cream and 1 cup of Parmesan cheese. Continue stirring until the cheese melts and creates a creamy sauce, about 2-3 minutes.
Remove from heat and let stand for 2-3 minutes to thicken. Top with remaining Parmesan and fresh parsley before serving.