Bring a large pot of salted water to a boil. Add the angel hair pasta and cook according to package instructions until al dente, about 3-4 minutes. Drain and set aside.
While the pasta cooks, heat the olive oil and 1 tablespoon of butter in a large skillet over medium heat.
Add the minced garlic and red pepper flakes to the skillet and sauté for about 1 minute until fragrant, stirring frequently to avoid burning.
Add the shrimp to the skillet in a single layer. Season with salt and freshly ground black pepper. Cook for 2-3 minutes on one side until pink and opaque, then flip and cook for another 1-2 minutes until fully cooked. Remove shrimp from skillet and set aside.
Add the chicken broth and lemon juice to the skillet. Bring to a simmer and cook for 2-3 minutes to reduce slightly.
Stir in the remaining 2 tablespoons of butter until melted and sauce is smooth.
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 the pasta is evenly coated with the sauce.
Remove from heat and stir in the chopped fresh parsley.
Adjust seasoning with additional salt and pepper if needed. Serve immediately.