Cook the Pasta
Bring a large pot of salted water to a boil. Cook the linguine according to package directions until al dente.
Reserve ½ cup of the pasta cooking water, then drain and set aside.
Prepare the Chicken
Season chicken cutlets with salt, pepper, and Italian seasoning.
In a large skillet over medium-high heat, add olive oil and butter.
Sear chicken on each side for 4–5 minutes, until golden brown and cooked through (internal temperature 165°F / 74°C).
Remove from skillet and keep warm.
Make the Alfredo Sauce
In the same skillet, melt 4 tbsp butter. Add garlic and sauté until fragrant (about 1 minute).
Pour in the heavy cream and bring to a gentle simmer.
Stir in Parmesan cheese until melted and smooth.
Season with salt, pepper, and nutmeg (if using).
Add reserved pasta water a little at a time to loosen the sauce if needed.