Season chicken breasts with salt and pepper, then cook in olive oil until golden brown and cooked through. Remove chicken, slice it, and set aside.

Cook fettuccine pasta according to package directions in a large pot of salted boiling water. Drain the pasta, reserving about a cup of the pasta water.

In the same skillet, melt butter and sauté minced garlic until fragrant. Pour in heavy cream and bring to a gentle simmer, stirring frequently.

Reduce heat to low, then gradually whisk in grated Parmesan cheese until the sauce is smooth and creamy. If the sauce is too thick, add a splash of the reserved pasta water.

Add the cooked fettuccine to the Alfredo sauce, tossing to coat evenly. Return the sliced chicken to the skillet and mix it with the coated pasta.

Serve immediately, garnished with chopped fresh parsley and additional Parmesan cheese if desired.