To prepare cake: Preheat oven to 350°F. Coat a 12-cup Bundt pan with cooking spray.
Whisk all-purpose flour, whole-wheat flour, granulated sugar, cocoa, baking powder, baking soda, pumpkin pie spice and salt in a medium bowl.
Blend 1 cup buttermilk, pumpkin puree and brown sugar in a large bowl with an electric mixer on low speed. Beat in whole egg and egg white. Stir in oil, corn syrup and vanilla. Gradually add the dry ingredients, stirring until just combined. Transfer the batter to the prepared pan.
Bake the cake until a wooden skewer inserted in the center comes out with only a few moist crumbs attached, 1 to 1 1/4 hours. Let cool on a wire rack for 15 minutes. Remove from the pan and let cool completely on the rack, about 2 hours.
To glaze & garnish cake: Combine confectioners' sugar and 1 tablespoon buttermilk in a small bowl, stirring until completely smooth. Place the cake on a serving plate and drizzle the glaze over the top; garnish with chocolate chips (or chopped nuts) while the glaze is still moist.
To warm an egg to room temperature, either set it out on the counter for 15 minutes or submerge it (in the shell) in a bowl of lukewarm (not hot) water for 5 minutes.To toast chopped nuts & seeds: Cook in a small dry skillet over medium-low heat, stirring constantly, until fragrant and lightly browned, 2 to 4 minutes.