In a slow cooker, add the hot water, brown sugar, butter, cloves, cinnamon sticks, cayenne pepper, and salt. Stir to combine, cover, then cook on low for 4 to 5 hours.

Add the rum, then stir to combine.

Ladle out the hot buttered rum into serving glasses, then top the drink with a sprinkle of nutmeg, cayenne pepper powder, and/or whipped cream. Add a cinnamon stick for garnish.