Preheat pizzelle baker according to manufacturer's instructions.
Mix whole wheat flour, baking powder, cinnamon, ginger, allspice, cloves, and black pepper together in a large bowl.
Melt butter in a large saucepan over medium heat. Remove from heat. Stir white sugar, brown sugar, molasses, and orange zest into saucepan until well-combined. Add 1/2 of the flour mixture, stirring until smooth. Add eggs; mix until smooth. Stir in remaining flour mixture, mixing until batter is smooth.
Drop spoonfuls of batter onto the preheated pizzelle baker. Bake until browned, about 1 1/2 minutes.