Heat 2 inches of olive oil in a large frying pan over medium heat until a deep-fry thermometer registers 325°.
While the oil is heating, put the buttermilk and the breadcrumbs in separate shallow bowls. Working in batches, dip the ravioli in the buttermilk to coat completely, allowing the excess buttermilk to drip back into the bowl. Dredge the ravioli in the bread crumbs. Place the ravioli on a baking sheet, while you coat the remaining ravioli.
When the oil is hot, fry the ravioli in batches, turning occasionally, until golden brown, about 3 minutes. Using a slotted spoon, transfer the fried ravioli to paper towels to drain.
Sprinkle the fried ravioli with Parmesan cheese and serve with a bowl of warmed marinara sauce for dipping.
Makes 4 to 6 servings.