Bring a large pot of salted water to a rolling boil over high heat. Add dry linguine and cook according to package instructions until al dente, about 8-10 minutes. Reserve 1 cup of the starchy pasta water before draining the pasta in a colander. Set the drained linguine aside.

In a large skillet, heat 2 tablespoons of olive oil over medium-high heat. Season the shrimp with salt and pepper. Once the oil is shimmering, add the shrimp in a single layer and cook until they turn pink and opaque, about 2-4 minutes. Remove the shrimp from the skillet and keep warm.

Lower the heat slightly and add 1 cup of heavy cream, 2 teaspoons of lemon zest, and a pinch of red pepper flakes to the same skillet. Allow to simmer for about 2 minutes, stirring occasionally, until thickened slightly.

Incorporate 2 tablespoons of unsalted butter into the sauce, whisking until completely melted and smooth. Gradually add 1/2 cup of finely shredded Parmesan cheese, stirring continuously until melted and creamy. Adjust seasoning with salt and pepper.

Add the cooked linguine to the creamy lemon sauce and pour in 1/4 cup of reserved pasta water. Squeeze in the juice of one fresh lemon and toss until well coated.

Fold the cooked shrimp back into the pasta and sauce mixture. Heat through for about 1 minute, then garnish with chopped parsley and serve warm.