Bring a large pot of water to a rolling boil, salt generously with about 1 tablespoon, and cook the fettuccine until just al dente, 9 to 11 minutes. Reserve 1/2 cup pasta water, then drain and toss the pasta with a drizzle of olive oil.
Pat the chicken dry, pound to an even 1/2-inch thickness if needed, and season both sides with kosher salt, black pepper, garlic powder, and Italian seasoning.
Heat olive oil in a large skillet over medium-high until shimmering. Sear the chicken 5 to 6 minutes per side until deep golden and the center reaches 165°F (74°C), then transfer to a cutting board and rest 5 minutes.
Lower heat to medium, melt the butter in the same skillet, and stir in the minced garlic for 30 seconds until fragrant. Pour in the heavy cream, scrape up the browned bits, and simmer gently for 2 to 3 minutes until slightly thickened.
Reduce heat to low or pull the skillet off the burner, then whisk in the grated Parmigiano Reggiano in two or three handfuls until smooth. Stir in the optional nutmeg and loosen with reserved pasta water as needed, then season to taste.
Toss the drained fettuccine in the skillet until fully coated, slice the rested chicken against the grain, and fan it over four plates of pasta. Finish with chopped parsley and extra Parmesan, and serve immediately.