Preheat the oven to 350°F. Spray an 8-inch square pan with olive oil cooking spray. Place 2/3 cup honey in a large glass measuring cup. Microwave on high power until the honey is runny and just bubbling, 45 to 60 seconds. Add ½ cup unsweetened cocoa powder and stir with a fork until well combined. Let cool to room temperature. Meanwhile, in a small bowl, place ½ cup white whole-wheat flour, ¼ tsp baking powder, ¼ tsp baking soda, and ¼ tsp salt. Whisk until well combined. In a large bowl, combine ½ cup unsweetened applesauce, 2 tbsp olive oil, 1 egg, and ¾ tsp vanilla extract. Whisk together until well blended. Add the honey-cocoa mixture and whisk until smooth. Add the flour mixture to the liquid mixture and stir until no traces of flour remain. Scrape the batter into the pan. Bake until the surface looks dry around the edges of the pan and a toothpick inserted in the center comes out with moist crumbs clinging to it, about 25 minutes. Let cool completely in pan before slicing into 16 squares.