Pour enough oil into a large frying pan to reach a depth of 1 inch. Heat the oil over medium heat until a deep-fry thermometer registers 325 degrees F.
While the oil is heating, put the buttermilk and the bread crumbs in separate shallow bowls. Working in three batches, dip ravioli in buttermilk to coat completely. Allow the excess buttermilk to drip back into the bowl. Dredge ravioli in the bread crumbs. Place the ravioli on a baking sheet, and continue with the remaining ravioli.
When the oil is hot, fry the ravioli in batches, turning once, until golden brown, about 3 minutes on each side. Using a slotted spoon, transfer the fried ravioli to paper towels to drain.
Sprinkle the fried ravioli with Parmesan and serve with warmed sauce for dipping.