Combine 1/2 cup whole wheat flour and self-rising flour in medium bowl. Mix in buttermilk. Knead dough on lightly floured surface 2 minutes. Cover and let rest 15 minutes.
Divide dough into 8 pieces. Roll 1 piece into smooth ball (keep remainder covered with towel). Dust generously with whole wheat flour and roll into 5-inch-diameter circle, dusting with flour to prevent sticking. Cover. Repeat with remaining dough.
Pour oil into wok or medium saucepan to depth of 3 inches. Heat to 375 degrees. Add 1 dough round to oil; dough will sink to bottom. When dough starts to rise, gently press in center with back of slotted spoon until bread puffs. Turn and cook until light brown, about 20 seconds. Transfer to paper towels using slotted spoon. Keep warm while cooking remaining dough. Place on platter and serve immediately.