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 2 tablespoons of butter and 2 tablespoons of olive oil in a large skillet over medium heat.
Add the minced garlic to the skillet and sauté for about 1 minute until fragrant, being careful not to burn it.
Add the shrimp to the skillet in a single layer. Season with salt, black pepper, and crushed red pepper flakes. Cook the shrimp for 2-3 minutes on one side until pink and opaque, then flip and cook for another 1-2 minutes until fully cooked. Remove the shrimp from the skillet and set aside.
In the same skillet, add the chicken broth and lemon juice. Bring to a simmer and cook for 2 minutes to reduce slightly.
Stir in the remaining 2 tablespoons of butter until melted and the sauce is smooth.
Return the cooked shrimp to the skillet and toss to coat in the sauce. Remove from heat.
Add the drained angel hair pasta to the skillet and gently toss to combine with the shrimp and sauce.
Sprinkle chopped fresh parsley over the top and adjust seasoning with salt and pepper if needed.
Serve immediately with lemon wedges on the side.