Bring a large pot of salted water to a boil, then add spaghetti and cook until just al dente, about 8 minutes. Drain, reserving a cup of pasta water, and set aside.
While the pasta cooks, peel and devein the shrimp if needed, then pat them dry with paper towels for better searing.
Heat a large skillet over medium-high heat and add 1 tablespoon of olive oil. Once shimmering, add the shrimp in a single layer. Sear for about 2 minutes per side until they turn pink and develop a light golden crust.
Remove the shrimp from the skillet and set aside. In the same skillet, add the remaining olive oil, then toss in the minced garlic and red pepper flakes. Cook gently for about 30 seconds until fragrant, stirring constantly to prevent burning.
Juice both lemons, then add the lemon juice and zest to the skillet. Stir quickly, scraping up any browned bits from the bottom of the pan to build flavor.
Return the seared shrimp to the skillet, tossing in the lemon-garlic sauce. Cook for about 1 minute, allowing the flavors to meld and the sauce to slightly thicken. If it becomes too thick, stir in a splash of the reserved pasta water.
Add the drained pasta to the skillet and toss everything together over low heat until evenly coated and heated through, about 1 minute. Season with salt and pepper to taste.
Sprinkle chopped parsley over the pasta, drizzle with a little olive oil, and give a final toss. Serve immediately with extra lemon wedges if desired, enjoying the bright, glossy dish.
