I've tried making Cacio e Pepe a few times, using a recipe from America's Test Kitchen. In Cacio e Pepe, you boil pasta in a limited amount of water, then mix some of the hot starchy water with grated pecorino Romano cheese. The cheese melts/dissolves in the water to form a cheesy liquid which is poured over the pasta.
I've had good luck doing this with Romano, even using domestic cow's milk Romano. But one time I was short on Romano, and tried using about 1/4th Romano and 3/4ths imported Parmesan. When I added the starchy water, some of the cheese dissolved--the Romano, I assume--but most of it coagulated into a gooey, stretchy mass.
What is the difference between Romano and Parmesan, that would make them behave so differently when mixed with hot, starchy water? Are there other similar cheeses--asiago for example--that would work well in this recipe?