Using an electric mixer, beat the brown sugar, butter, honey, cinnamon, nutmeg, cloves, and salt in a medium bowl until blended and smooth. Transfer the mixture to a 4-cup (or larger) measuring cup. Add the rum and then 2 cups of boiling water. Stir until the butter mixture dissolves. Divide the buttered rum among 4 mugs. Garnish with the cinnamon sticks and serve.