Preheat oven to 350°F. Spray an 8" square pan with olive oil. Set aside.
Place the honey in a large glass measuring cup. Microwave on high power until the honey is runny & just bubbling, 45 to 60 seconds. Add cocoa & stir with a fork until well combined. Let cool to room temperature.
Meanwhile, in a small bowl, place the flour, baking powder, baking soda, & salt. Whisk until well combined.
In a large bowl, combine the applesauce, oil, egg, & vanilla. Whisk together until well blended. Add honey, cocoa mixture & whisk until smooth. Add the flour mixture to the liquid mixture & stir until no traces of flour remain. Scrape the batter into the prepared pan.
Bake until the surface looks dry around the edges of the pan & a toothpick inserted in the center comes out with moist crumbs clinging to it, about 25 minutes. Do not overbake. Place the pan on a cooling rack & let cool completely before slicing into 16 squares.
Store the brownies in an airtight container at room temperature for up to 3 days.
Melt 1 c. sugar in heavy skillet over low heat, stirring constantly. Heat until melted to a golden brown syrup, stirring constantly. Remove from heat. Add boiling water & stir over low heat until lumps are dissolved. Pour into measuring cup ¼ c. of caramel mixture & add enough cold water to make 1 c. of liquid.
Cream together the softened shortening & remaining sugar until fluffy. Beat in thoroughly eggs. Sift together the flour, baking powder, & 1 tsp. salt. Stir in alternately with caramel mixture. Pour into two 9" layer pans or 13"x9" oblong pan & bake 35 minutes in preheated 350°F oven.
Heat together remaining caramel mixture, cream, & butter to make the burnt sugar frosting. Beat in the powdered sugar, salt, & vanilla extract.