Preheat oven to 325 degrees F. Coat a 10-inch springform pan with cooking spray.

Place dates in a small bowl. Pour boiling water over them to soak. Let cool to room temperature.

Process whole-wheat flour, all-purpose flour, 2/3 cup walnuts, baking soda and salt in a food processor until the walnuts are completely ground and the mixture resembles coarse meal. Transfer to a medium bowl; make a well in the center.

Puree the dates and soaking water in the food processor until smooth, scraping down the sides as necessary. Add egg, 3/4 cup syrup, oil, butter, 2 teaspoons vinegar and vanilla and process until smooth and creamy. Scrape the date mixture into the well in the dry ingredients and stir together gently until just combined. Transfer to the prepared pan.

Bake the cake until a skewer inserted in the center comes out clean, 30 to 35 minutes. Transfer to a wire rack and let cool completely. Run a knife around the edges to loosen the cake, if necessary, and remove the sides of the pan.

To glaze cake: Carefully lift the cake from the pan bottom and place on a cake stand or serving plate. Whisk maple syrup, vinegar and confectioners' sugar in a small bowl. Add water, 1 teaspoon at a time, if necessary to make a spreadable consistency. Spread the glaze evenly over the top of the cake, then decorate with the remaining 1/3 cup walnuts.

Tip: To toast chopped walnuts: Cook in a small dry skillet over medium-low heat, stirring constantly, until fragrant and lightly browned, 2 to 4 minutes.

MAKE AHEAD TIP: Prepare through Step 5 up to 8 hours ahead. Glaze and decorate the cake (Step 6) when ready to serve.