Slice the polenta. Open the polenta tube and remove the wrapper. Cut off the rounded ends (optional). Slice the polenta into ½-inch thick rounds, about 20 total. Pat each round dry on both sides with a paper towel.
Season the rounds. Sprinkle both sides of the polenta rounds with ½ teaspoon kosher salt and ¼ teaspoon black pepper.
Set up the breading station. In three shallow bowls, place: (1) the all-purpose flour, (2) the beaten eggs, and (3) the breadcrumbs, parmesan, ½ teaspoon kosher salt, ½ teaspoon black pepper, oregano, and garlic powder whisked together.
Bread each round. Dredge each polenta round lightly in flour and shake off the excess. Dip into the beaten egg, letting the excess drip back into the bowl. Press both sides firmly into the parmesan-breadcrumb mixture to coat fully.
Preheat the air fryer to 380°F (193°C) for 2-3 minutes. Lightly spray the basket with olive oil.
Air fry the polenta cakes. Arrange breaded polenta rounds in a single layer with space between each (work in batches as needed). Mist the tops with olive oil. Cook at 380°F for 12-15 minutes, flipping halfway through and spraying the second side with oil. The cakes are done when both sides are deeply golden and crispy.
Rest on a wire rack. Transfer cooked polenta cakes to a wire cooling rack — not a plate — to keep the bottoms crispy.
Plate and serve. Smear warm marinara sauce on each serving plate. Arrange the polenta cakes on top. Scatter arugula or fresh basil over the cakes. Tear burrata into pieces and tuck it between and on top of the polenta. Finish with flaky sea salt, cracked black pepper, and a drizzle of good olive oil. Serve immediately.