1To brine the chicken, in a large gallon-sized zippered plastic bag, combine the buttermilk, salt, garlic, and oregano. Close the bag and shake to combine. Add the chicken and place in a shallow bowl or dish. Cover and refrigerate for 4–8 hours.
2In a large, heavy saucepan or Dutch oven, pour oil to a depth of 2–3 inches. Heat over high heat to 325°F on a deep-frying thermometer. Place a large wire rack on a rimmed baking sheet next to the stove.
3While the oil is heating, in a large bowl, whisk together the flour, chili powder, cumin, and baking powder. Remove the chicken from the brine, letting the excess drip off. Add the chicken, a few pieces at a time, to the flour mixture and toss to coat evenly, then transfer to a baking sheet.
4When the oil is ready, add about half the chicken pieces to the hot oil. Adjust the heat to keep the oil around 325°F. Fry, turning occasionally with tongs, until golden brown and cooked through, about 15 minutes. Using a slotted spoon or a spider, transfer the chicken to the rack. Repeat with the remaining chicken.