I'm not sure this is what you are looking for. I don't think you can make a brownie exclusively with honey and come out with a texture that is right. I have made this one and, as I recall, I think you want to be careful not to over bake.
Honey bear Brownies
1 1/2 cup sugar
3/4 cup unsweetened cocoa
3/4 cup butter, melted
3/4 cup honey
1 Tablespoon vanilla
4 eggs
1 cup all purpose flour
1/2 tsp. salt
Cream sugar and melted butter. Add honey, vanilla, eggs and mix in. Mix in dry ingredients until just incorporated. Don't over beat. Pour into greased 8x8 or 9x9 inch pan. Bake at 350 degrees.
A note about the icing recipe that I started this thread with, I do recall that it only makes about 1 cup. I always double it.
I have a really good honey buttercream recipe that I posted on another beekeeping website. I'll get it and post it here too. It's really good.