Measure the honey into a large glass measuring cup (at least 2-cup-size). Microwave on high until the honey is runny and just bubbling, about 1 minute. Add the cocoa and stir with a fork until well combined. Let cool to room temperature.
Meanwhile, in a small bowl, whisk together the flour, baking powder, baking soda, and salt.
In large bowl, whisk together the applesauce, oil, egg, and vanilla. Add the honey-cocoa mixture and whisk until smooth. Add the flour mixture and stir until no traces of flour remain. Scrape the batter into the prepared pan.
Bake for about 25 minutes, until the surface looks dry around the edges of the pan and a toothpick inserted near the center comes out with moist crumbs. Do not over bake. Place the pan on a cooling rack and let cool before slicing in squares. Store the brownies in an airtight container at room temperature for up to 3 days.
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