Bring a large pot of salted water to a boil, cook fettuccine until al dente, reserve ½ cup pasta water, then drain and set aside.
Pat chicken dry, season with salt, pepper, and Italian seasoning. Heat olive oil in a skillet over medium-high, cook chicken 6–7 minutes per side until golden and 165°F inside. Rest 5 minutes, then slice into strips.
In the same skillet, melt butter over medium heat. Sauté minced garlic 1–2 minutes until fragrant. Gradually whisk in heavy cream and milk, simmer about 5 minutes until slightly thickened. Stir in Parmesan until smooth, season with salt and pepper.
Toss pasta in the Alfredo sauce, add a splash of reserved pasta water if needed. Top with sliced chicken, sprinkle with parsley and extra Parmesan, and serve hot.