Heat oven to 450° F. Toss the bread crumbs with 2 tablespoons of the oil, ½ teaspoon salt, and ¼ teaspoon pepper until well coated. Bake on a rimmed baking sheet, tossing once, until golden brown, 3 to 5 minutes. Transfer to a shallow bowl. Place the flour and eggs each in separate shallow bowls.
Rub the remaining oil on 2 rimmed baking sheets. Working one at a time, dip the onion rings in the flour, then in the eggs (letting any excess drip off), then coat with the bread crumbs, turning and pressing gently to help them adhere. Bake on the prepared baking sheets, flipping the onion rings once, until tender, 12 to 14 minutes.
Whisk together the buttermilk, mayonnaise, chipotles, parsley, and ¼ teaspoon salt in a small bowl. Serve with the onion rings for dipping.