Season the shrimp with salt and pepper. Heat 1 tablespoon of olive oil in a large skillet or pan over medium-high heat. Add the shrimp and cook until they are pink and opaque, about 2 minutes per side. Remove the shrimp from the pan and set aside.
Add the chicken broth and heavy cream to the pan and bring to a simmer. Break the fettuccine in half if necessary to fit it into the pan. Submerge the pasta in the liquid as much as possible.
Cook the pasta, stirring occasionally, for about 12-15 minutes, or until the pasta is al dente and the liquid has reduced to a creamy sauce. You may need to adjust the heat to maintain a gentle simmer.
Combine and Finish:
Once the pasta is cooked, stir in the grated Parmesan cheese until melted and the sauce is smooth. Add the cooked shrimp back into the pan, tossing to coat them in the sauce and heat through.
Serve:
Taste and adjust seasoning with additional salt and pepper if needed. Serve the shrimp fettuccine Alfredo hot, garnished with chopped fresh parsley.