Cook spaghetti according to package instructions. Drain and set aside.
In a large skillet, melt 2 tbsp butter over medium heat. Add shrimp, season with salt and pepper, and cook until pink, about 2-3 minutes per side. Remove shrimp and set aside.
In the same skillet, melt remaining 2 tbsp butter. Add garlic and cook until fragrant, about 1 minute.
Stir in chicken broth, heavy cream, and Parmesan. Simmer for 3-4 minutes until thickened.
Add cooked spaghetti and shrimp back to the skillet. Toss to coat.