Bring a large pot of salted water to a boil. Cook the fettuccine according to the package until al dente. Reserve 1/2 cup of the pasta water, then drain and set pasta aside.

Season the chicken strips evenly with 1/2 teaspoon salt and 1/4 teaspoon pepper.

Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add the chicken in a single layer. Sear for 5–7 minutes, turning occasionally, until golden and cooked through. Remove chicken to a plate and tent with foil.

Reduce heat to medium. In the same skillet, melt 3 tablespoons unsalted butter. Add 3 cloves minced garlic and cook about 1 minute until fragrant. Do not brown the garlic.

Pour in 1 1/2 cups heavy cream and bring to a gentle simmer. Slowly whisk in 1 cup freshly grated Parmesan until the sauce is smooth. Stir in 1/4 teaspoon nutmeg if using.

Taste the sauce and adjust seasoning with salt and black pepper. Return the cooked chicken to the skillet and toss to coat.

Add drained fettuccine and toss until everything is evenly coated. Add reserved pasta water a tablespoon at a time to loosen the sauce if needed.

Serve immediately, garnished with 2 tablespoons chopped parsley and extra grated Parmesan.