Preheat oven to 350°F. Place a 9-inch round metal baking pan in the oven to heat.
Beat egg in a large heatproof mixing bowl. Add syrup, white whole-wheat flour, all-purpose flour and salt; mix well to blend. Stir in butter.
Combine boiling water and baking soda in a bowl, then pour into the batter; stir just to combine.
Carefully coat the preheated pan with cooking spray. Pour the batter into the pan. Top with pecan halves.
Bake the cake until a knife inserted in the center comes out with a few crumbs attached to it, 30 to 32 minutes. Cool in the pan on a wire rack for 30 minutes. Serve warm with whipped cream, if desired.