Working with one rabbit loin at a time, place the jackrabbit between two sheets of plastic wrap or parchment paper, or place into a gallon-size Ziploc bag. Pound the jackrabbit until thin using a meat mallet, the bottom of a heavy skillet, or a rolling pin. Start in the center of the rabbit loin and work your way out. Aim for ¼-inch thickness.
Use a sharp knife to cut each rabbit loin into 3 pieces so you have a total of 6 nicely tenderized rabbit steaks.
Season both sides of each rabbit steak with salt and black pepper.
Place flour in a large, shallow bowl. Whisk together buttermilk, eggs, paprika, onion powder, and cayenne pepper in a second large, shallow bowl. Stir together cornflakes and 1 teaspoon salt in a third large, shallow bowl.
Working with one rabbit steak at a time, dredge rabbit in flour, shaking to remove excess. Dip in buttermilk mixture, letting excess drip off. Dredge in cornflakes, and press down to adhere. Transfer coated rabbit steaks to a large plate.
Add oil to a large (12-inch) skillet or Dutch oven and heat over medium-high until shimmering. Fry rabbit, 3 pieces at a time, until the edges start to look golden brown, about 2 minutes each side, adjusting heat lower as needed. Remove fried jackrabbit and transfer to the rimmed baking sheet with wire rack and transfer to preheated 200 degree oven to keep warm while frying remaining jackrabbit. Repeat until all the rabbit is cooked.
Make the Gravy
After all the rabbit is fried, pour off the oil into a bowl. Without cleaning the skillet, return it to the stove over medium-low heat. Add ¼ cup of the oil back to the skillet and allow it to heat up (discard remaining oil).
Add flour to oil and whisk constantly for 1 minute. Whisk in buttermilk, heavy cream, salt, black pepper, and onion powder. Cook, whisking constantly, until bubbling and thickened, about 3 minutes. Remove from heat.
Serve chicken fried jack rabbit smothered with gravy with green beans on the side, if so desired. Sprinkle with a little more black pepper.