Bring a large pot of salted water to a boil. Cook the fettuccine until al dente. Before draining, reserve 1 cup of the pasta water.
Pat the chicken dry and season both sides with salt and black pepper. Sear in 1 tablespoon butter over medium heat, about 4 to 5 minutes per side, until golden and cooked through. Rest a few minutes, then slice.
In the same skillet over medium-low heat, melt 4 tablespoons butter and cook the garlic for about 30 seconds. Pour in the heavy cream, basil, oregano and optional ground nutmeg and warm it through.
Take the pan off the heat and whisk in the grated Parmesan a handful at a time until smooth.
Add the drained pasta and toss to coat, loosening with reserved pasta water until glossy. Return the sliced chicken, season to taste, and serve hot.
Notes
Grate the Parmesan from a block. Pre-shredded cheese can make the sauce grainy. Keep the sauce below a simmer after the cheese goes in to prevent breaking. Reserved pasta water is your best tool for loosening a too-thick sauce.