Note: Refrigerating the coated rings for between 1 and 4 hours helps the breading to adhere to the onion during baking and eating—so don’t skip that step!
LINE two large rimmed baking pans with parchment paper.
MAKE THE ONION RINGS: In a large bowl, combine the almond flour, paprika, oregano, salt, and garlic powder. In another large bowl, whisk the 2 eggs. Stir ¼ cup of the flour mixture into the eggs.
SEPARATE the onion slices into rings. Add 3 to 4 onion rings at a time to the egg mixture and turn to coat. Use your hands or a slotted spoon to transfer the onions to the flour mixture; turn to coat.
TRANSFER the onions to the baking pans in a single layer. Refrigerate for at least 1 hour or up to 4 hours.
MAKE THE AIOLI: In a blender, combine the green onions, egg, garlic, mustard, and lemon juice. Cover and pulse to combine. With the blender running, slowly add the light olive oil until creamy. Add the pepper and pulse to combine. Transfer to a serving bowl; cover and refrigerate until ready to serve.
PREHEAT the oven to 450°F. Drizzle the onion rings with the extra-virgin olive oil. Bake until the onions are tender and the coating is golden and crisp, about 20 minutes. Transfer to a serving platter and serve with the aioli.