Bring a large pot of salted water to a boil.
Add the angel hair pasta and cook until al dente, about 4-5 minutes.
Drain the pasta, reserving 1/2 cup of pasta water.
In a large skillet, heat 2 tablespoons of olive oil over medium heat.
Add the shrimp, season with salt and pepper, and cook until pink, 2-3 minutes per side.
Remove shrimp from the skillet and set aside.
In the same skillet, add the remaining olive oil and minced garlic.
Cook until garlic is fragrant, about 1 minute.
Add the white wine and red pepper flakes to the skillet.
Simmer for 2-3 minutes.
Add the butter and lemon juice, stirring until the butter is melted.
Add the cooked pasta and shrimp back into the skillet.
Toss to combine, adding reserved pasta water if the sauce seems dry.
Remove from heat and stir in chopped parsley and grated Parmesan cheese.
Serve immediately.