To prepare cake: Preheat oven to 350 degrees F. Coat an 8-inch-square glass baking dish with cooking spray and dust it with flour, shaking out the excess.

Spread walnuts on a baking sheet and toast, stirring once halfway, until fragrant, about 7 minutes. Transfer to a plate to cool. Reduce oven temperature to 325 degrees .

Whisk whole-wheat flour (see Measuring Tip), barley flour, baking powder, cinnamon, cloves, baking soda, nutmeg and salt in a large bowl. Whisk eggs and brown sugar in a medium bowl until thoroughly blended. Combine yogurt with orange zest and juice in a small bowl and stir until smooth; gradually whisk into the egg mixture along with oil. Add the wet ingredients to the dry ingredients in 2 additions, stirring well in between until just blended. Fold in 1 cup of the walnuts. Spread the batter into the prepared pan.

Bake the cake until a wooden skewer or toothpick inserted into the center comes out with just a few moist crumbs attached, 35 to 45 minutes.

To prepare syrup: Meanwhile, combine ⅓ cup orange juice, ¼ cup brown sugar, orange zest strip and cloves in a small heavy saucepan; bring to a boil over medium-high heat, stirring a few times. Adjust heat to maintain a simmer and cook until thickened, 4 to 5 minutes (you will have a scant ⅓ cup); remove the zest and cloves. Let cool.

When the cake is done, transfer the pan to a wire rack. Using a toothpick, pierce the top in about 18 places and brush the syrup over the cake 3 or 4 times, allowing it to seep in each time. Sprinkle with the remaining ¼ cup walnuts and let cool for 30 minutes; loosen the edges with a knife; cut into 12 squares. Enjoy warm or room temperature.