Begin by bringing a large pot of salted water to a rolling boil. Add the fettuccine pasta and cook according to package instructions until al dente, typically around 8-10 minutes. Once cooked, reserve a cup of pasta water for later and then drain the pasta in a colander. Set it aside while you prepare the shrimp and broccoli.

In a large skillet, melt 2 tablespoons of butter over medium-high heat. Add minced garlic and sauté for about 30 seconds until fragrant. Then, add the shrimp and cook for 2-3 minutes until they turn pink and opaque. Next, toss in the broccoli florets and sauté them for an additional 3-4 minutes until tender-crisp and vibrant green, stirring occasionally.

Pour in 1 cup of heavy cream into the skillet with the shrimp and broccoli, and bring the mixture to a gentle simmer over medium heat. Once it starts to bubble lightly, gradually stir in freshly grated Parmesan cheese, continually whisking until it melts into a creamy sauce. This will take about 2-3 minutes; aim for a smooth, velvety texture.

Add the cooked fettuccine to the skillet with the Alfredo sauce, tossing everything together to coat the pasta thoroughly. If the sauce appears too thick, gradually add reserved pasta water until the desired creaminess is reached. Season generously with salt and pepper to taste, stirring well so every strand of pasta is evenly coated.

Carefully plate the Shrimp and Broccoli Alfredo while it's hot, ensuring that each serving has a good amount of shrimp and broccoli nestled among the pasta. If desired, garnish with extra Parmesan and freshly cracked black pepper. Serve immediately alongside garlic bread and a fresh salad for a delightful meal.