Bring a large pot of salted water to a rolling boil. Add the spaghetti and cook until al dente, about 8 minutes. Drain, reserving ½ cup of pasta water, and set aside.
While the pasta cooks, heat 2 tablespoons of olive oil in a large skillet over medium heat. Add the minced garlic and sauté until fragrant, about 30 seconds, until it turns a light golden hue.
Sprinkle the chili flakes into the garlic oil and cook for another 10 seconds until sizzling. Be careful not to burn the garlic. Remove the garlic and chili flakes from the pan and set aside.
Increase the heat to medium-high and add the shrimp to the skillet. Sear for about 2 minutes per side, until they turn pink and opaque. Use a slotted spoon to remove the shrimp and set aside.
Lower the heat to medium, add the broth to the skillet, and scrape up any browned bits from the bottom. Let it simmer for 2 minutes, releasing a fragrant, spicy aroma.
Add the cooked pasta to the skillet and toss to coat in the flavorful sauce. Pour in a little of the reserved pasta water to loosen the sauce and make it glossy, stirring gently.
Return the cooked shrimp to the skillet, gently tossing everything together. Squeeze fresh lemon juice over the dish, then sprinkle with chopped parsley. Toss once more to combine all the bright flavors.
Check the seasoning and adjust with more chili flakes or salt if needed. Serve immediately in warm bowls, garnished with extra parsley and lemon wedges if desired.
