Fill a large pot with well-salted water and bring it to a rolling boil. Add the linguine and cook until just al dente according to the package directions, usually about 8 to 10 minutes. Before draining, scoop out roughly 1/2 cup of the starchy pasta water and set it aside.

Heat the olive oil in a large skillet over medium-high heat. Add the shrimp in a single layer and season lightly with salt and black pepper. Cook for 2 minutes per side until the shrimp are pink and opaque, then transfer them to a plate and set aside.

Reduce the heat to medium and keep the same skillet. Add the garlic and red pepper flakes, stirring for about 30 seconds until fragrant and just softened, being careful not to brown the garlic. Pour in the chicken broth and lemon juice, scraping up any browned bits from the bottom of the pan. Let the mixture simmer for 2 to 3 minutes, or until slightly reduced.

Return the shrimp to the skillet and toss gently to coat them in the sauce. Add the drained linguine to the skillet and toss everything together until the pasta is evenly coated. If the sauce looks dry, add a splash of the reserved pasta water to loosen it up.

Remove the skillet from the heat and stir in the fresh parsley. Taste and adjust the seasoning with additional salt and pepper if needed. Serve immediately with grated Parmesan cheese on top for an extra layer of savory flavor.