Season chicken cutlets with Italian seasoning, garlic powder, salt, and pepper. Heat olive oil in a large skillet over medium-high heat. Cook chicken for 4-5 minutes per side until golden and cooked through (165°F). Transfer to a plate and tent with foil.
Meanwhile, bring a large pot of water to a rolling boil. Add salt and cook fettuccine until al dente according to package directions. Reserve 1 cup of pasta water, then drain the pasta.
In the same skillet over medium-low heat, melt butter. Add minced garlic and sauté for 30 seconds until fragrant, being careful not to brown it. Pour in heavy cream and bring to a gentle simmer, whisking constantly.
Reduce heat to low. Gradually whisk in the Parmesan cheese until melted and smooth. Add nutmeg if using, then season with salt and white pepper. If too thick, thin with a splash of reserved pasta water until it reaches a velvety consistency.
Slice the rested chicken into strips. Toss the drained fettuccine directly into the sauce, using tongs to coat every strand. Divide among plates, top with sliced chicken, and garnish with extra Parmesan and chopped parsley.