Start by boiling a large pot of salted water. Add your linguine and cook it until it’s just al dente, following the instructions on the package. Before draining, scoop out about half a cup of the pasta water and save it—you may need it to loosen up the sauce later.
Pat your chicken breasts dry and season them evenly with salt, black pepper, and Italian seasoning. Heat olive oil in a large skillet over medium heat. Place the chicken in the pan and cook for about 5–6 minutes on each side, or until they’re golden and fully cooked through. Set them aside to rest before slicing.
In the same skillet (no need to wash!), reduce the heat to medium-low and melt the butter. Toss in the minced garlic and stir until fragrant—about 30 seconds. Pour in your coconut milk or cream, whisking as it heats. Let it simmer for a few minutes until slightly thickened.
Add the freshly grated Parmesan to the creamy mixture and stir until it melts into a silky sauce. Season with a bit more salt and black pepper. Then add your cooked linguine into the pan and toss everything until the noodles are fully coated. If the sauce feels too thick, pour in a little of that reserved pasta water until it loosens up.
Slice the rested chicken and serve it over the creamy pasta. Finish with a sprinkle of extra Parmesan, chopped parsley or chives, and a final crack of black pepper.