Cook the fettuccine in salted boiling water according to package directions until al dente, then drain and set aside.
Heat olive oil in a large skillet over medium-high heat and cook the chicken strips for 6 to 8 minutes, turning once, until golden and cooked to 165°F / 74°C, then transfer to a plate.
Reduce heat to medium, add butter and garlic to the same skillet, and cook for 1 minute until fragrant.
Pour in the heavy cream, bring to a gentle simmer, and cook for 3 to 4 minutes until slightly thickened.
Stir in the Parmesan cheese, black pepper, and nutmeg, whisking until the sauce is smooth and creamy.
Add the cooked fettuccine and chicken to the skillet and toss gently until everything is evenly coated with the Alfredo sauce.
Serve immediately with extra Parmesan on top if desired.