Heat olive in a medium pan over medium heat. Add garlic and stir until fragrant, 1 to 2 minutes. Add butter and stir constantly until melted. Pour in chicken broth; add pepper and salt. Bring to a boil. Add spaghetti and cook, stirring occasionally, until tender yet firm to the bite, about 12 minutes. Add more chicken broth if pasta starts to stick to the pan.
Stir Parmesan cheese, cream, and parsley into the pasta and mix thoroughly. Serve immediately.