Preheat oven to 325°. Coat a 10-inch springform pan with cooking spray. Place dates in 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 food processor until walnuts are completely ground and mixture resembles coarse meal. Transfer to medium bowl; make a well in center.
Puree dates and soaking water in food processor until smooth, scraping down sides as necessary. Add egg, 3/4 cup syrup, oil, butter, 2 teaspoons vinegar and vanilla and process until smooth and creamy. Scrape date mixture into well in dry ingredients and stir together gently until just combined. Transfer to prepared pan. Bake cake until skewer inserted in center comes out clean, 30 to 35 minutes. Transfer to a wire rack and let cool completely. Run knife around edges to loosen cake, if necessary, and remove sides of the pan. To glaze cake: Carefully lift cake from pan bottom and place on 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 glaze evenly over top of cake, then decorate with 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. Equipment: 10-inch springform pan
Nutrition bonus: High omega-3s.