Boil a large pot of salted water. Cook the fettuccine until al dente, about 10–12 minutes. Drain and set aside, saving some pasta water.
In a large skillet, melt the butter over medium heat. Add minced garlic and stir for 1–2 minutes until fragrant and lightly golden—don’t let it burn.
Pour in the heavy cream and stir to combine. Let it simmer gently for 3–5 minutes, stirring occasionally, until slightly thickened.
Lower the heat and add grated Parmesan. Stir until smooth and creamy. Add a splash of pasta water if the sauce gets too thick.
Fold in the lump crabmeat carefully to keep the pieces intact. Season with salt and pepper. Heat for 2–3 minutes until warmed through.
Add the cooked fettuccine to the skillet. Gently toss with tongs to coat the pasta evenly. Add more pasta water if needed to loosen the sauce.
Serve hot, topped with chopped fresh parsley for color and brightness.