Bring a large pot of salted water to a boil. Add the linguine and cook according to package instructions until al dente, usually about 9-11 minutes. Reserve 1/4 cup of pasta water before draining, then drain the pasta and set aside.
In a large skillet over medium heat, melt 2 tablespoons of the butter. Add minced garlic and red pepper flakes, stirring frequently. Cook for about 1-2 minutes until fragrant but not browned.
Add the peeled and deveined shrimp to the skillet. Season lightly with salt and pepper. Cook for 2-3 minutes on each side until the shrimp turn pink and opaque. Remove the shrimp from the skillet and set aside.
Reduce heat to low. Add the remaining 2 tablespoons of butter to the skillet, along with the chicken broth and lemon juice. Stir well, scraping up any browned bits from the bottom of the pan. Let the sauce simmer for 2-3 minutes to reduce slightly.
Return the shrimp to the skillet, then add the cooked linguine. Toss everything together, adding reserved pasta water a little at a time if the sauce seems too thick. Adjust salt and pepper to taste.
Remove from heat and stir in chopped fresh parsley. Serve immediately with a generous sprinkle of grated Parmesan cheese on top. For an extra kick, add an additional pinch of red pepper flakes if desired.