Boil the taro in generously salted water until a fork easily passes through the taro. Drain and let them cool enough to handle, then peel the skin off each tuber. Pass them through a food mill or potato ricer, then add the pecorino and flour. Knead until the flour is incorporated, but be careful not to over-work it. The dough should be on the soft side, and will get sticky if you let it sit.
Heat a large pot of water to boil the gnocchi. Generously flour a work surface, then cut off a piece of dough and roll it out into a thin rope about 1/4"-1/2" thick. If it gets sticky just put down some more flour. Use a sharp knife to cut off 1" pieces of dough and place in a single layer on a sheet pan.
To prepare the sauce, put the cream in a small saucepan and heat over medium low heat until small bubbles start to form at the edges of the pot (it should not be boiling). Toss the grated Gruyere with the cornstarch, then add the mixture to the heated cream and whisk together until the cheese has completely melted and the sauce has thickened slightly. Keep the sauce warm, but do not let it boil, or it will separate.
Add the gnocchi to your boiling water in about 3 batches. Give the gnocchi about 20 seconds after they start floating to the top before transferring them to a colander using a slotted spoon. Toss the boiled gnocchi with the cream sauce, adjust the salt to taste, then serve immediately.