To Brine the Rabbit: In a large bowl, whisk together buttermilk, salt, mustard powder, paprika, black pepper, garlic powder, onion powder, rosemary, and thyme. Add rabbit pieces and toss to thoroughly coat. Transfer contents of bowl to a 1-gallon zipper-lock freezer bag and refrigerate for at least 8 hours and up to 12 hours, flipping bag occasionally to redistribute the contents and coat rabbit evenly.
To Dredge and Fry: Adjust oven rack to middle position and preheat oven to 200°F (95°C). Set a wire rack in a rimmed baking sheet. In a large bowl, whisk together flour, salt, and pepper. Working with one piece of rabbit at a time, remove rabbit from marinade, allowing excess buttermilk to drip off, and add to flour mixture. Toss to thoroughly coat, pressing with your hands to get flour to adhere to rabbit in an even layer. Transfer to prepared wire rack, and repeat dredging process with remaining rabbit pieces. Let dredged rabbit rest for 15 minutes.
Meanwhile, line a second rimmed baking sheet with paper towels and set a clean wire rack in it. Heat oil in a 12-inch cast iron skillet or 14-inch wok over medium-high heat to350°F (175°C). Carefully add half the rabbit pieces and fry, adjusting heat to return to a 350°F (175°C) frying temperature, until golden brown on the first side, about 8-10 minutes. Using tongs, carefully flip rabbit pieces, and continue to fry until golden brown all over, and thickest part of rabbit registers 160°F (70°C) on an instant-read thermometer, about 7 minutes longer. Transfer fried rabbit to prepared wire rack, season lightly with salt, then transfer to oven to keep warm.
Skim any browned bits from oil and discard. Return oil to 350°F (175°C), and repeat with remaining rabbit. Let rest 5 minutes. Serve.
