Bring a large pot of salted water to a boil and cook the linguine according to package instructions until al dente. Reserve 1 cup of pasta cooking water, then drain the pasta.
While the pasta cooks, pat the shrimp dry and season lightly with salt and pepper.
Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat. Add the shrimp and cook 1 to 2 minutes per side until pink and just cooked through. Transfer shrimp to a plate.
Reduce heat to medium, add remaining butter to the skillet, then add minced garlic and red pepper flakes. Cook until fragrant, about 30 seconds, taking care not to burn the garlic.
Stir in lemon juice and 1/2 cup of the reserved pasta water, scraping any browned bits from the pan. Add drained pasta to the skillet and toss to combine. If needed, add more pasta water a little at a time to loosen the sauce.
Return the shrimp to the pan, add Parmesan and chopped parsley, and toss until everything is coated and heated through. Taste and adjust seasoning with salt and pepper.
Serve immediately with extra Parmesan and lemon wedges on the side.
Notes
For a lighter version, substitute half the pasta with zucchini noodles. Freshly grated Parmesan yields the best flavor.