Bring a large pot of salted water to a boil. Cook spaghetti according to package instructions until al dente. Drain and set aside.
While the pasta cooks, heat olive oil in a large skillet over medium-high heat.
Add shrimp to the skillet, season with salt and black pepper, and cook for 2-3 minutes on each side until pink and opaque. Remove shrimp from skillet and set aside.
In the same skillet, reduce heat to medium and add butter. Once melted, add minced garlic and red pepper flakes. Sauté for 1-2 minutes until fragrant.
Pour in white wine and chicken broth, scraping the bottom of the skillet to release any browned bits. Simmer for 3-4 minutes until the sauce reduces slightly.
Return shrimp to the skillet and toss to coat in the sauce. Cook for an additional 1-2 minutes to heat through.
Add the cooked spaghetti to the skillet and toss to combine with the shrimp and sauce.
Remove from heat and stir in grated Parmesan cheese and chopped parsley.
Adjust seasoning with salt and black pepper to taste.
Serve immediately.