Line a baking sheet or counter with three layers of paper towels and set a wire rack on top to drain the fried ravioli.
Pour canola oil into a deep frying pan or pot to a depth of about 2 inches and heat over medium until a deep-fry thermometer reads 325°F (about medium heat).
In a shallow bowl, whisk together the slightly beaten eggs and milk until smooth.
In a separate shallow bowl, combine the Italian seasoned breadcrumbs and Panko breadcrumbs.
Working in batches, dip each ravioli into the egg-milk mixture, letting excess drip off, then coat thoroughly in the breadcrumb mixture.
Fry 3–5 ravioli at a time (depending on pan size) for 1–3 minutes, stirring and flipping often with a spoon or spider, until crispy and golden brown.
Transfer fried ravioli to the prepared wire rack and sprinkle each with freshly grated Parmesan.
Repeat breading and frying until all ravioli are cooked, then serve warm with marinara or your favorite dipping sauce.