Slice the onion into 1/4-inch rings and separate the rings from each other. Place the onions in a large bowl and cover with the buttermilk, then sprinkle with salt. Let marinate, refrigerated, at least 2 hours or up to overnight, if possible.
In a food processor, pulse the chicharrons to a sandy consistency.
Add the baking powder, 2 cups flour and a sprinkle of salt to a shallow dish. Add the eggs to another shallow dish and whisk to combine. Mix the smoked paprika and remaining 1 1/2 cups flour with the crushed chicharrons in a third shallow dish. Line a sheet tray with a wire rack.
Toss a batch of the marinated onion slices in the flour mixture until they are well coated. Place the flour-coated onions into the egg and coat. Dip the rings into the chicharron mix to coat. Place on the wire rack and repeat with the remaining rings. Reserve, chilled and uncovered, at least 30 minutes or up to 1 hour in the refrigerator.
Preheat the oven to 450 degrees F.
For the sauce: Add the jalapenos and onions to a 14-inch cast-iron pan or sheet tray. Drizzle with 1/4 cup oil and sprinkle with salt and pepper. Roast until slightly charred, about 10 minutes.
Meanwhile, in a nonreactive bowl, mix together the mayonnaise, sweetened condensed milk and smoked paprika until well combined. Transfer the roasted onions and jalapeno to a food processor and process until fully combined. Add this to the mayonnaise mixture and stir until fully combined. Adjust the seasoning as needed.
Heat the remaining quart peanut oil in a wide-bottomed pot or fryer to 375 degrees F. Line a sheet tray with a wire rack.
Fry the onion rings in batches, being careful not to overload, until golden brown and floating, 3 to 4 minutes. Drain on the wire rack-lined sheet tray and season with salt.
Serve hot with the dipping sauce.
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