Preheat oven to 350°. Coat a 10-inch Bundt cake pan with spray.
Combine flours, baking powder, baking soda, salt, and 1 cup sugar in a large bowl.
Whisk next 7 ingredients (through vanilla) in another large bowl until blended. Add to the dry ingredients and stir with a spatula until just combined. Transfer 3/4 cup batter to a small bowl and whisk in chocolate, cocoa, and remaining 1 tablespoon sugar. Pour 3 cups white batter into prepared pan. Dollop chocolate batter over white batter; cover with remaining white batter. Using a knife, swirl batter once in a continuous S-shape around pan.
Bake 55 minutes, until a skewer inserted in the center comes out clean. Cool in pan 10 minutes; invert onto rack and cool completely.
In a bowl, combine glaze ingredients and drizzle over cake. Serve.