Bring a large pot of salted water to a boil. Cook fettuccine according to package directions until al dente. Reserve 1/2 cup pasta water, then drain.
Season chicken breasts with salt and pepper on both sides.
Heat olive oil in a large skillet over medium-high heat. Sear chicken for 5 to 7 minutes per side until the internal temperature reaches 165°F (74°C). Remove from pan, let rest for 5 minutes, and slice into strips.
In the same skillet over medium heat, melt the butter.
Add minced garlic and sauté for 1 minute until fragrant.
Whisk in the heavy cream and bring to a gentle simmer. Cook for 3 to 5 minutes until slightly thickened.
Reduce heat to low and gradually whisk in the Parmesan cheese until melted and the sauce is smooth.
Add the cooked fettuccine to the sauce. Toss to coat, adding reserved pasta water as needed to adjust consistency.
Top with sliced chicken and garnish with chopped parsley before serving.