Heat oven to 350 degrees Fahrenheit and grease an 8x8 dish with olive oil, coconut oil or avocado oil.
In a small bowl or measuring cup, mix together the honey and cocoa powder with a fork or whisk until well combined. You may need to warm the honey slightly to make it more stir-able.
In another bowl, mix together the dry ingredients (flour, baking powder, baking soda and salt).
In another large mixing bowl, whisk together the wet ingredients (apple sauce, oil, egg and vanilla). Once well combined, pour in the chocolate and honey mixture and stir all wet ingredients together until you get an even consistency.
Add the flour mixture (dry ingredients) to the combined wet ingredients. Stir gently until no traces of the dry mixture remain.
Add the brownie batter to your prepared baking pan.
Bake just until the surface looks dry around the edges. Do not overcook, as this will yield a dryer brownie. With this recipe in an 8x8 pan, it should take about 13 minutes. However, if you tried different flours or if you doubled or tripled the recipe, you will need to watch it carefully to suit the pan, flour and amount of batter you made. You can insert a toothpick in the center and it should come out with some moist crumbs on it.
Let brownies cool completely before slicing into them.