Bring a large pot of salted water to a boil. Add angel hair pasta and cook according to package instructions until al dente, about 3 to 4 minutes. Drain and set aside.
While pasta cooks, heat olive oil and 2 tablespoons of butter in a large skillet over medium heat.
Add minced garlic and red pepper flakes to the skillet and sauté for about 1 minute until fragrant, stirring constantly to avoid burning.
Add shrimp to the skillet in a single layer. Season with salt and freshly ground black pepper. Cook shrimp for 2 to 3 minutes on one side until pink and opaque, then flip and cook for another 1 to 2 minutes until fully cooked. Remove shrimp from skillet and set aside.
Pour chicken broth into the skillet and bring to a simmer. Let it reduce slightly for about 2 minutes.
Stir in the remaining 1 tablespoon of butter, lemon juice, and lemon zest. Mix well to combine and create a light sauce.
Return the cooked shrimp to the skillet and toss to coat in the sauce.
Add the drained angel hair pasta to the skillet and gently toss everything together until pasta is evenly coated with the shrimp scampi sauce.
Remove from heat and sprinkle chopped fresh parsley over the top.
Serve immediately, garnished with extra parsley if desired.