Cook the linguine pasta according to package instructions in salted boiling water until al dente. Reserve 1/2 cup of the pasta water, then drain and set aside.
In a large skillet, heat the olive oil and butter over medium heat. Once melted, add the minced garlic and sauté for about 1 minute until fragrant, being careful not to burn it.
Add the shrimp to the skillet and season with salt, pepper, and red pepper flakes (if using). Cook for about 2-3 minutes on each side until the shrimp turns pink and opaque. Remove the shrimp from the skillet and set aside.
In the same skillet, pour in the heavy cream and bring to a gentle simmer. Stir in the grated Parmesan cheese, and mix until the sauce is creamy and smooth.
Add the cooked linguine and the reserved pasta water to the skillet, tossing to combine and coat the pasta with the creamy sauce.
Gently fold in the cooked shrimp and let everything cook together for about 2 more minutes until heated through.
Taste and adjust seasoning with more salt, pepper, or red pepper flakes if desired.
Serve hot, garnished with chopped parsley for freshness.
Notes
Adjust seasoning to taste and garnish with fresh parsley.