Cut each onion crosswise into 1/4-inch-thick slices. Separate the slices into individual rings; remove the 4 small center rings from each slice and reserve them for another use.
Soak the onions.
Put the separated onion rings into a large baking dish or shallow bowl and cover them with the buttermilk.
Make the beer mustard.
In a small bowl, whisk the aioli, dijon mustard, agave syrup, cinnamon, beer-extract powder and cayenne until combined. Set aside.
Make the batter.
In a large bowl, whisk 1 cup all-purpose flour, the rice flour, seltzer, beer and honey until smooth. Put the remaining 2 cups all-purpose flour in a separate large bowl or shallow pan and season it generously with kosher salt.
Fry the onion rings.
Fill a large heavy pot with at least 3 inches of vegetable oil. Attach a deep-fry thermometer to the side of the pot and heat the oil over medium-high heat to 350 degrees F.
Working in batches, lift the onion rings from the buttermilk and shake off the excess. Transfer them to the flour mixture and toss until coated, then dip one by one into the beer batter, shaking off the excess, and add to the hot oil.
Fry, turning the onions often with tongs, until golden brown, 3 to 4 minutes; adjust the heat as necessary to maintain the oil temperature.
Drain and serve.
Drain the onion rings on paper towels and sprinkle with parsley and flaky salt while still warm. Serve with the beer mustard.