Heat a large pan over medium heat and add 2 tablespoons of butter.
Cook the shrimp for 1 to 2 minutes per side until pink and opaque, then remove and set aside.
Add the remaining butter to the pan and sauté the minced garlic for 30 seconds until fragrant.
Pour in chicken broth and milk, then add the fettuccine noodles, breaking them slightly if needed to fit.
Stir to separate the noodles, bring to a boil, cover, reduce heat, and simmer for 10 to 12 minutes, stirring occasionally until pasta is tender.
Remove the lid, reduce heat to low, and stir in the heavy cream, Parmesan cheese, salt, pepper, and nutmeg until sauce is creamy and cheese melts.
Return the shrimp to the pan and gently stir to coat them in the sauce.
Remove from heat and let the dish sit for 5 minutes to thicken before garnishing with fresh parsley and serving warm.