Roasted sweet potato gives these biscuits their moist texture and orange hue.
Preheat oven to 425°F. Line a small baking pan with foil and a baking sheet with parchment paper.
Poke sweet potato all over with a fork and place on the foil-lined pan. Roast until tender, about 40 minutes. Let stand until cool enough to handle, about 15 minutes. Slice open, scoop out the flesh and mash until smooth. Refrigerate the mashed sweet potato. Increase oven temperature to 450°F.
Meanwhile, place kale, 1 tablespoon oil, lemon juice and ¼ teaspoon salt in a large bowl. Rub the kale until it turns a darker shade of green and reduces in volume. Set aside.
Combine all-purpose flour, whole-wheat flour, baking powder and 1/2 teaspoon salt in a large bowl. Add butter and use a pastry blender or 2 knives to cut it into the flour mixture until pea-size lumps form.
Combine buttermilk and the mashed sweet potato in a medium bowl or measuring cup. Make a well in the middle of the flour mixture and gradually pour in the sweet potato mixture. Gently fold the mixture into the flour with a flexible spatula. Stop mixing just when there is no dry flour visible and the dough begins to pull away from the sides.
Divide the dough into 8 pieces and roughly shape into biscuits. Space the biscuits 2 inches apart on the prepared baking sheet. Bake until light golden on top, about 15 minutes. Transfer the biscuits to a wire rack and let cool for 15 minutes.
Heat the remaining 1 tablespoon oil in a large nonstick skillet over medium heat. Crack all 8 eggs into the pan and cook for 1 minute. Cover the pan and cook until the whites are set, but the yolks are still runny, 1 to 2 minutes more. Remove from heat. Sprinkle the eggs with chives, pepper and the remaining ¼ teaspoon salt. Partially cover to keep warm.
Slice the biscuits. Place a piece of Cheddar on each of the bottom halves and top with an egg and some of the kale. Cover with the biscuit tops.
Equipment: Parchment paper