Cook the pasta: Bring a pan of salted water to the boil. Use just enough water to cover the fettuccine so it becomes as starchy as possible. Cook until al dente and drain, reserving a mugful of the pasta water.
Sear the chicken: Butterfly each breast and flatten to 1cm thick between cling film with a rolling pin. Season with salt and pepper, brush with oil. Sear on a hot griddle or frying pan for 2 to 3 minutes on each side until golden. Rest for 2 minutes, then slice into strips.
Brown the butter: In a large sauté pan, melt the butter over a high heat. Let it foam and turn golden brown until it smells sweet and nutty, about 3 minutes. Remove from the heat and stir in the garlic.
Build the sauce: Pour in a ladleful of the reserved pasta water. Return to the heat. Add the drained fettuccine and the Parmesan, tossing until the cheese melts and coats every strand. Add more pasta water if needed. Season with black pepper.
Serve: Divide the pasta between warm bowls. Lay the sliced chicken on top. Finish with extra Parmesan and a twist of pepper.
