In a skillet, melt the butter and add the pepper, letting the pepper infuse the butter as it melts. Stir in the flour and cook for about three minutes, until completely smooth and incorporated.
Pour in the milk in a thin stream while whisking. It might start out lumpy, but keep whisking and it will smooth out into a thick paste. Stir in the pecorino in batches, and remove from the heat. The sauce will be very thick.
Bring a pot of salted water to a boil and cook the pasta according the packaging or until it is al dente.
Take 1/4 cup of the hot starchy pasta water and stir it into the cacio e pepe sauce, whisking over medium low heat until smooth and glossy. Add the drained pasta, stirring in extra pasta water as needed until the sauce coats the pasta. Enjoy with extra pepper and crushed red peppers, if desired.