Cook the pasta: Boil linguine in salted water until al dente. Drain and set aside. Save 1/4 cup of pasta water.
Cook the shrimp: Heat olive oil and butter in a large pan over medium heat. Add garlic and stir for 30 seconds.
Add shrimp: Season shrimp with salt, pepper, and red pepper flakes. Add to the pan and cook 1–2 minutes per side until pink and curled.
Make the sauce: Pour in broth, lemon juice, and zest. Stir and let simmer for 1–2 minutes.
Toss pasta: Add cooked pasta to the pan. Toss well to coat. Add a splash of pasta water if needed.
Finish and serve: Top with fresh parsley and Parmesan if desired. Serve immediately.