Cook the Pasta: In a large pot of salted boiling water, cook the linguine according to package instructions until al dente. Reserve about 1 cup of pasta water, then drain the pasta and set aside.
Add Liquids: Pour in the chicken or vegetable broth, heavy cream, and the juice and zest of the lemon, stirring well to combine. Bring the mixture to a simmer and let it cook for about 5 minutes, allowing it to thicken slightly.
Combine Pasta and Spinach: Add the cooked pasta and chopped spinach to the skillet with the creamy sauce. Toss to combine everything thoroughly, adding reserved pasta water a little at a time until you reach your desired sauce consistency.
Finish and Serve: Stir in the grated Parmesan cheese and return the cooked shrimp to the skillet. Mix well and allow it to heat through for another 2 minutes. Taste and adjust seasoning with salt and pepper, if necessary.
Garnish and Plate: Serve the creamy shrimp pasta hot, garnished with freshly chopped parsley and additional lemon zest if desired.
Notes
Adjust seasoning to taste. Fresh parsley and lemon zest make great garnishes.