Bring a large pot of salted water to a boil. Cook the fettuccine according to package instructions until al dente, about 10-12 minutes. Drain and set aside, reserving 1/2 cup of pasta water.
While the pasta cooks, heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Season the chicken pieces with salt and black pepper, then add them to the skillet. Cook for 5-7 minutes, stirring occasionally, until golden and cooked through (internal temperature of 165°F/74°C). Remove the chicken and set aside.
In the same skillet, add the remaining 1 tablespoon of olive oil. Add the minced garlic and sauté for 1 minute until fragrant, being careful not to burn it.
Reduce the heat to medium. Add the butter and let it melt, then pour in the heavy cream. Stir constantly for 2-3 minutes until the mixture begins to simmer. Add the Parmesan cheese, stirring until it melts and the sauce thickens, about 3-4 minutes. Season with salt, black pepper, and nutmeg (if using).
Return the cooked chicken to the skillet, then add the drained fettuccine. Toss everything together until the pasta is well coated in the sauce. If the sauce is too thick, add a splash of reserved pasta water to reach your desired consistency.
Remove from heat and transfer to serving plates. Garnish with fresh parsley if desired. Serve your creamy chicken Alfredo hot and enjoy a rich, comforting dinner!