Heat the oven to 375°F with racks in the upper- and lower-middle positions. Line 2 rimmed baking sheets with kitchen parchment. In a small microwave-safe bowl, stir together the currants and 2 tablespoons water.

Microwave uncovered on high until warm and plump, about 30 seconds; set aside. In a medium bowl, toss the kale and lemon juice; set aside. In a large bowl, whisk together the flour, sugar, baking powder, baking soda, salt and pepper.

To a food processor, add about half of the flour mixture and scatter all of the butter over the top. Pulse until the butter is in pieces slightly larger than peas, 10 to 12 pulses. Transfer to the bowl with the remaining flour mixture.

Add the currants and any remaining liquid, the cheddar, pecorino and kale. Toss with your hands until well combined. Add about ⅓ of the buttermilk and toss just a few times with your hands, making sure to scrape along the bottom of the bowl, until the liquid is absorbed.

Add the remaining buttermilk in 2 more additions, tossing after each. After the final addition of buttermilk, toss until no dry, floury bits remain. The mixture will be quite crumbly and will not form a cohesive dough.

Lightly dust the counter with flour, turn the mixture out onto it, then give it a final toss. Divide it into 2 even piles, gathering each into a mound, then briefly knead each mound; it's fine if the mixture is still somewhat crumbly.

Gather each mound into a ball, then press firmly into a cohesive 5-inch disk about 1½ inches thick. Using a chef's knife, cut each disk into 6 wedges.

Place 6 wedges on each prepared baking sheet, spaced evenly apart. Brush the tops with the beaten egg, then sprinkle with the sunflower seeds, pressing lightly to adhere.

Bake until the scones are deep golden brown, 30 to 35 minutes, switching and rotating the baking sheets halfway through. Cool on the baking sheets on wire racks for 5 minutes, then transfer directly to a rack and cool for at least another 5 minutes. Serve warm or at room temperature.