Heat about 1–2 inches of olive oil in a deep skillet or pot over medium heat until it reaches 350°F–360°F (or a small piece of bread sizzles and browns in about 30–45 seconds).
Pour the buttermilk into a large shallow bowl.
Place the flour in a gallon-size resealable bag and the breadcrumbs in a separate bowl or bag; add the grated Parmesan to the breadcrumbs and mix.
Working in batches of about 8–10 ravioli, dip the ravioli into the buttermilk, turning to coat all sides.
Transfer the wet ravioli to the bag with flour, shake to coat, then return them briefly to the buttermilk to re-wet the surface.
Place the ravioli into the breadcrumb-Parmesan mixture, toss or shake to fully coat, and shake off any excess.
Carefully add the breaded ravioli to the hot oil in a single layer (do not overcrowd) and fry until golden brown, about 1–2 minutes per side.
Use tongs or a slotted spoon to transfer fried ravioli to a paper towel-lined plate to drain, then sprinkle with additional grated Parmesan if desired.
Repeat the breading and frying process with the remaining ravioli, then serve immediately with marinara for dipping.