Bring a large pot of salted water to a boil and cook the fettuccine until it is tender but still firm to the bite. Drain the pasta, saving one cup of the cooking water.
Heat a large skillet over medium heat and cook the ground beef, breaking it up as it browns. Season with salt and pepper and cook through.
Move the beef to the side of the pan and add the minced garlic; cook for about 60 seconds until it releases its aroma.
Pour in the heavy cream and slowly whisk in the Parmesan cheese until the sauce becomes smooth and creamy.
Stir in the fresh spinach and cook until the leaves have just wilted, scraping the pan bottom to mix in any tasty bits.
Add the drained pasta to the skillet and toss everything together, using reserved pasta water to loosen the sauce to your preferred consistency. Serve immediately while hot.