Cook the pasta. If serving over noodles, boil the linguine in salted water until al dente. Reserve 1/2 cup of pasta water, then drain.
Season the shrimp. Pat the shrimp dry and season lightly with salt and pepper.
Sear the shrimp. Heat the olive oil and 2 tablespoons of butter in a large skillet over medium-high heat. Cook the shrimp 1–2 minutes per side, until pink and opaque (internal temp 145°F), then move them to a plate.
Build the base. Lower the heat to medium, add the garlic and red pepper flakes, and stir for about 30 seconds until fragrant.
Deglaze without wine. Pour in the broth and lemon juice, scraping up browned bits. Simmer 2–3 minutes to reduce slightly.
Finish the sauce. Turn off the heat and swirl in the remaining 2 tablespoons of butter until glossy.
Combine and serve. Return the shrimp (and pasta) to the pan, add lemon zest and parsley, and toss. Add reserved pasta water if the sauce needs loosening.