Cook the pasta according to the package instructions. Drain the pasta, reserving about 1 cup of pasta water, and set aside.
If using large shrimp, cut into smaller pieces. Lightly salt your shrimp. Set aside.
In a large skillet, melt the butter over medium heat. Add the minced garlic and cook for about 1-2 minutes until fragrant.
Add the raw shrimp to the skillet and cook for 2-3 minutes on each side until they turn pink and are cooked.
Reduce the heat to low to medium, pour in the heavy whipping cream and stock of your choice. Stir well and let it simmer for a couple of minutes until slightly thickened.
Stir in the lemon juice and lemon zest, then add the grated Parmesan cheese. Season with salt and pepper to taste.
Add the cooked pasta to the skillet and toss gently until it's well coated with the sauce. If the sauce is too thick, you can add a splash of reserved pasta water to adjust the consistency.
Serve the garlic shrimp lemon pasta hot, garnished with additional grated Parmesan cheese and fresh parsley or green onions (if desired).