Preheat oven to 325 degrees. Line two baking sheets with parchment paper and set aside.
In a small saucepan, combine honey, Sugar In The Raw®, and butter over medium heat. Stir constantly until butter is melted and sugar is dissolved. Remove from heat and allow to cool.
In the bowl of an electric mixer, gently whisk together 2 cups of flour and the baking soda. Switch to paddle attachment. Add in egg yolk, rum, vanilla extract, and the cooled honey mixture. Beat on medium until well combined. Slowly add in the remaining cup of flour until dough loses it's stickiness and becomes a ball.
Flour a work surface and roll dough to 1/4 inch thick. Using a 4 inch gingerbread man cookie cutter, cut out the dough.
Place cookies on prepared sheets and bake for 12 minute or until centers are set and edges are just turning golden brown. Allow cookies to cool for 5 minutes on baking sheet and remove to a wire rack to cool completely.
Decorate with icing and sugar. Serve and enjoy!
Store any leftover cookies in an airtight container for up to 7 days.