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 crushed red pepper flakes to the skillet. Sauté for about 1 minute until fragrant, being careful not to burn the garlic.
Add the shrimp to the skillet in a single layer. Season with salt and freshly ground black pepper. Cook for 2-3 minutes on each side until the shrimp turn pink and are cooked through. Remove shrimp from the skillet and set aside.
Pour the white cooking wine into the skillet. Bring to a simmer and cook for 2-3 minutes until the liquid reduces slightly.
Stir in the remaining 2 tablespoons of butter, lemon juice, and lemon zest. Stir until the butter melts and the sauce is well combined.
Return the cooked shrimp to the skillet and toss to coat in the sauce.
Add the drained angel hair pasta to the skillet. Toss gently to combine and heat through for 1-2 minutes.
Remove from heat and sprinkle the chopped fresh parsley over the pasta and shrimp. Adjust seasoning with salt and pepper if needed.
Serve immediately, garnished with extra lemon wedges if desired.