Bring a large pot of salted water to a boil. Add the fettuccine and cook according to package instructions until just al dente. Reserve about 1/2 cup of pasta water, then drain the pasta and set aside.
Pat the scallops dry with paper towels to ensure a nice crust. Season lightly with salt and pepper. Heat 2 tablespoons of butter over medium-high heat in a large skillet. When the butter is foaming, add the scallops in a single layer. Cook for about 2-3 minutes per side without moving them, allowing a golden crust to form. Remove scallops from the skillet and set aside.
Reduce the heat to medium and add the remaining 2 tablespoons of butter to the skillet. Add the minced garlic and sauté for about 1 minute until fragrant but not browned. Pour in the chicken broth to deglaze the pan, scraping up any browned bits from the scallops. Let it simmer for 2-3 minutes to reduce slightly.
Lower the heat and stir in the heavy cream. Let the sauce simmer gently until it thickens, about 3-4 minutes. Stir in the grated Parmesan cheese until melted and smooth. Season with salt and pepper to taste.
Add the cooked fettuccine to the skillet with the sauce. Toss gently to coat the pasta evenly, adding reserved pasta water as needed to loosen the sauce. Return the scallops to the pan to warm through for a minute or so.
Remove from heat and sprinkle the chopped fresh parsley over the top. Serve immediately, savoring the luxurious flavors and tender textures.