Bring a large pot of well-salted water to a boil. Cook the spaghetti according to package instructions until it reaches an al dente texture. Reserve approximately 1 cup of the pasta water before draining. Drain the pasta and set it aside.

Pat the shrimp dry using paper towels to remove excess moisture. Season both sides with salt and pepper. In a large skillet, heat olive oil over medium-high heat. Add the shrimp and cook for approximately 2 minutes per side, until they become pink and firm. Remove the shrimp from the skillet and set aside.

Reduce the skillet's heat to medium-low. Add minced garlic and red pepper flakes (if using) to the skillet and sauté for approximately 1 minute until fragrant. Stir in the lemon zest, lemon juice, and broth. Allow the mixture to simmer and reduce slightly for approximately 2 minutes.

Gradually add the heavy cream to the skillet, stirring continuously until thoroughly combined. Slowly incorporate the Parmesan cheese in small increments, ensuring it melts smoothly into the sauce. If the sauce appears too thick, gradually add reserved pasta water until it reaches the desired consistency.

Return the cooked pasta and shrimp to the skillet. Toss all components together until the pasta is evenly coated with the sauce. Taste the dish and adjust seasoning with additional salt and pepper, if necessary.

Transfer the prepared pasta to serving plates. Garnish with chopped parsley, additional Parmesan cheese, and lemon slices as desired. Serve promptly and enjoy.