Preheat oven to 350 degrees. Coat an 8-inch square glass baking dish with cooking spray and dust it with flour. Shaking out the excess. Walnuts: Toast walnuts on a baking sheet, stirring once halfway, until fragrant, about 7 minutes. Transfer to a plate to cool.

Reduce oven temperature to 325.

Cake: Whisk dry ingredients together 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 toothpick inserted into the center comes out with just a few moist crumbs attached, 35 to 45 minutes.

Syrup: Combine syrup ingredients in a small heavy saucepan; bring to a boil over medium-high heat, stirring a few times. Maintain a simmer and cook until thickened, 4 to 5 minutes (you will have a scant 1/3 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 walnuts and let cool.