Bring a large pot of heavily salted water to a boil and cook fettuccine until al dente according to package instructions.
While pasta cooks, season chicken breasts with salt and pepper on both sides.
Heat olive oil in a large skillet over medium-high heat and sear chicken for 5-7 minutes per side until the internal temperature reaches 165°F (74°C).
Remove chicken from the skillet and let rest for 5 minutes before slicing into thin strips.
In the same skillet, reduce heat to medium and melt the butter.
Add minced garlic to the butter and sauté for 1 minute until fragrant.
Pour in the heavy cream and bring to a gentle simmer, whisking occasionally for 3-5 minutes until slightly thickened.
Reduce heat to low and gradually whisk in the grated Parmesan cheese until completely melted and smooth.
Stir in the ground nutmeg and additional salt or pepper to taste.
Drain the pasta, reserving 0.25 cup of the starchy cooking water.
Toss the fettuccine and sliced chicken into the sauce, adding reserved pasta water if needed to reach desired consistency.
Garnish with fresh parsley and serve immediately.