Heat a few inches of olive oil in a large skillet or deep fryer over medium heat until it reaches 350°F (or is hot enough that a breadcrumb sizzles immediately).
Set up a dredging station with the buttermilk in one bowl, the flour in a second bowl or gallon bag, and the breadcrumbs in a third bowl or bag.
Working in batches of about 10 ravioli, dip each ravioli in the buttermilk so all sides are wet.
Place the wet ravioli in the flour and toss or shake to coat, then return them to the buttermilk to re-moisten all sides.
Transfer the ravioli to the breadcrumbs and press or shake so each piece is evenly coated with breadcrumbs.
Carefully add the breaded ravioli to the hot oil in a single layer (do not overcrowd) and fry until golden brown, 1–2 minutes per side.
Use tongs or a slotted spoon to remove the ravioli and drain on a paper towel–lined plate; sprinkle with grated Parmesan while hot.
Repeat the breading and frying process with remaining ravioli and serve immediately with marinara for dipping.