Blackberry-Lime Cornmeal Shortcakes

• 1 cup (125 g) all-purpose flour
• 1/2 cup (40 g) medium-grind cornmeal
• 2 teaspoon baking powder
• 1/4 teaspoon kosher salt
• 3 tablespoon granulated sugar
• 2 teaspoon finely grated lime zest
• 4 tablespoon unsalted butter, frozen until hard
• 1/2 cup plus 1 tablespoon (120 ml) cold heavy cream
• 1 1/2 teaspoon demerara sugar, for sprinkling
• 4 cup (440 g) fresh blackberries
• 1/4 cup plus 1 teaspoon (65 g) granulated sugar, divided
• 1 tablespoon fresh lime juice
• 1 cup cold, heavy cream
• additional lime zest, for garnish

1. Preheat the oven to 375 degrees. Line a baking sheet with parchment.
2. In a large bowl, whisk the flour, cornmeal, baking powder, salt, granulated sugar, and zest. Using the large holes on a box grater, grate the butter over the dry ingredients. Fluff gently with a fork. Drizzle with the ½ cup (118 ml) of the cream. Stir with a wooden spoon just until the ingredients cohere and no visible floury bits remain.
3. Transfer the dough to a floured board and form into a 4 ½-inch diameter, 1-inch-high disc. Cut into quarters and transfer to a baking sheet. Brush with the remaining tablespoon of cream and sprinkle with the Demerara sugar. Bake the shortcakes until golden, risen, and firm to the touch, 18-20 minutes. Transfer to a rack to cool completely. Cut in half horizontally.
4. Toss the blackberries with ¼ cup (62 g) of the sugar and lime juice. Transfer ½ of the mixture to a small bowl and set aside. Take a potato masher to the remaining blackberry mixture and mash until pulpy. In a large bowl, whip the cream to soft peaks with the remaining 1 teaspoon of sugar.
5. To assemble, lay 1 shortcake bottom on a plate. Dollop with some whipped cream, top with a few whole berries, replace the shortcake cap, and spoon some of the mashed blackberry pulp on top. Garnish with lime zest. Repeat with the remaining shortcakes, berries, cream, and zest. Serve immediately.