½ teaspoon ground cloves, preferably freshly ground;
½ teaspoon baking soda;
½ teaspoon fine sea salt;
¾ cup extra-virgin olive oil;
¾ cup freshly squeezed orange juice;
¾ cup packed light or dark brown sugar;
½ cup chopped toasted walnuts;
3 tablespoons turbinado or granulated sugar, for sprinkling;
Confectioners’ sugar, for dusting.
Position a rack in the center of the oven and preheat to 350°F. Butter an 8-inch square glass baking dish, or coat with cooking spray. Dust with flour, shaking out any excess.
Combine the raisins and the brandy in a small bowl to plump, stirring once or twice while you prep the ingredients.
Whisk together the white whole wheat flour and barley flour, 1 teaspoon of the cinnamon, cloves, baking soda, and salt in a large bowl. Make a well in the center. Place the olive oil, orange juice, and brown sugar in a medium bowl. Beat vigorously with a large whisk until the sugar dissolves and the mixture thickens slightly and becomes opaque, about 2 minutes. Pour the olive oil mixture into the center of the dry ingredients and stir with a spatula until just combined. Do not overmix. Fold in the plumped raisins along with any liquid, and then the walnuts.
Scrape the batter into the prepared pan, evening out the top with a spatula. Combine the turbinado sugar with the remaining ¼ teaspoon cinnamon in a small bowl and sprinkle over the cake. Bake until a cake tester or wooden skewer inserted into the center comes out clean, about 40 minutes.
Transfer the pan to a wire rack to cool for about 10 minutes. Loosen around the edges with a small sharp knife, unmold, and return the cake to the wire rack right side up to cool completely. Just before serving, dust generously with confectioners’ sugar. Cut into 9 or 12 pieces.
TO GET A HEAD START: Don’t hesitate to bake this cake 1 day ahead, as its flavors deepen. Store in an airtight container at room temperature.